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ASPECTS OF PITCH AND PITCH-CLASS ORGANIZATION
IN NIKOLAI ROSLAVETS'S TROIS COMPOS IT IONS POOR PIANO (1914)
By
DAVID WILLIAM MCISAAC
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ARTS
MUSIC THEORY
i n
THE FACULTY OF GRADUATE STUDIES
(Department o-f Music)
We accept this thes'i/S as con-forming
to the. -required standard
THE UNIVERSITY OF BRITISH COLUMBIA
July 1986
© David William McIsaac, 1986 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Department of Music .
The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3
Date July, 1986
DE-6 rvR-n i i
ABSTRACT
Nikolai Andreevich Roslavets (1881-1944) is a unique figure in Russian avant-garde musical developments o-f this century.
His system of tonal organization,
. similar to Scriabin's reliance on a central chordal complex . . . was based on chords of six to eight or more tones, used . . . as substitutes for the functional relationships of classical tonality, which he did not reject but rather tried to expand. These "synthetic chords" of specific and invariable interval lie structure could be transposed not only to the seven pitches of the classical diatonic scale, but also to all twelve degrees of the chromatic scale. Through systematic application of such trans• positions, Roslavets's compositions revealed elements similar to dodecaphonic serial thinking as early as 1914-15. . . . (Detlef Gojowy, "Half Time for Nikolai Roslavets," in Russian and Soviet Musics Essays for Boris Sctowarz , 212. )
Trois Compositions pour piano (1914) exhibit such charac•
teristics. Gojowy *s Neue sov/jetische Musi A der 20er Jahret and
George Perle's Serial Composition and Atonality both include limited references to Trois Compositions as well as general com• mentary about Roslavets's compositional techniques. However, detailed studies of pitch and pitch-class (PC) organization in music by this little-known composer are lacking. Proceeding
•from the analyses of Gojowy and Perle, the present thesis exam• ines certain aspects of Roslavets's "synthetic chord" system
(designated in the thesis as the interval-c1 ass complex or ICC system) in Trois Compositions, including: (1) PC contents of harmonies in the pieces--contents based on transposition-1evels
(T-levels) of ICCs associated with the pieces—and variances thereof, some of which are related to the forms of the pieces; iii
(2) harmonic successions and associated T-levelss (3) rhythmic aspects of these T-levels and their successions, which indicate a basis o-f hierarchy of T-levelss (4) characteristics of T-level successions as to PC content, and PC invariance and pitch conti• nuity involving adjacent T-levels, particularly T-levels related by interval-c1 ass (IC) 3s and (5) patterns of linear and verti• cal ordering of PCs as to their inclusion in particular T-lev• els. These are discussed in Chapter Two, following an introduc• tion to Roslavets and his music in Chapter One.
In consideration of Roslavets's position as a post-Romantic composer, other compositional techniques and tendencies evident in Trois Compositions are investigated in the thesis. Chapter
Three involves an examination of tonality in the three pieces, while Chapter Four involves a study of octatonicism and serial- ism, some characteristics of which are to be found in Trois
Compositions. i v
TABLE OF CONTENTS
Abstract • ••• ii
List o-f Examples and Figures vii
Acknowledgements xi
Chapter One: Introduction ...... 1 Biographical Information...... 1 Aspects o-f Roslavets's Compositional Style and Techn i que •• 4 Notes 10
Chapter Two: The Interval-C1 ass Complex in Trots Compos i t ions. 15 Introduction and Terminology.. .15 The ICC in Trois Compos f t ions. 22 ICC of "I" 22 ICC Of "II" 30 ICC of "III" 34 Harmonic Successions and Successions o-f Transposition-Levels 44 Transpositional Relationships o-f Adjacent T-Levels 44 Transpositional Cycles o+ T-Levels...... 46 " I " 47 "II" . . 51 "III" 52 T-Level Occurrences and Their Rhythmic Characteristics: Towards a Hierarchy o-f T-levels 54 Harmonic Rhythm o-f "I" 55 Harmonic Rhythm o-f "II" 57 Harmonic Rhythm o-f "III" 59 Hierarchy o-f T-Levels .62 T-Level Occurrences and Their Relationships to Form: "I" 64 "II" 65 "III" 66 Recurrent Harmonic Successions 67 Characteristics o-f T-Level Occurrences as to PC Content 71 PC Invariance and Pitch Continuity 71 PC Invariance in IC-3-Related T-Levels.. 85 V
Element Occurrence and Ordering in Trois Compos i t i ons ...... 91 Linear Element Occurrence and Ordering: "I" 91 "II" .93 "111 "... 93 Element occurrence in bass lines 95 Vertical Element Occurrence and Ordering in Individual Harmonies: "I" 95 "II" 99 "III" lOl "I", "II", and "III" as a whole 104 Vertical Element Adjacencies 105 Conclusion 113 Notes 117
Chapter Three: Tonality in Trois Compositions .125 Introduction 125 Tonality in "I" 127 Surface Tonal Features 127 Midd1eground/Background Linear Structures o-f "I" 131 Initiating single-pitch exposure. 131 Linear structures in "I" 134 Melodic fragments 136 Bass-line linear structures 137 Middleground/BacWground Harmonic Structures of "I" 139 Tonality in "II" 140 Surface Tonal Features .140 Midd1eground/Background Linear Structures of "II" 146 Diminished-seventh linear structures in mm. 6-9. 146 Mi dd1eground/Background Harmonic Structures of "II" 150 Tonality in "III" 151 Surface Tonal Features 151 Midd1eground/Background Linear Structures of "III"... 154 Midd1eground/Background Harmonic Structures of "III" 157 Conclusion 159 Notes 161 v i
Chapter Four: Other Systems o-f Pitch-Class Organization in Trois Compositions 165 Serial PC Organization .168 Serial Ordering of T-Levels and o-f PCs in T-Levels 170 Serial Ordering o-f Melodic Pitches 172 Notes 175
Chapter Five: Conclusion 178 The ICC System 178 Tonality, Octatonicism, and Serial ism. 180 Implications o-f "III" Concerning Matters o-f Style and Large-Scale Form.. 181
Selected Bibliography... 183
Appendix A: Chronological List o-f Works by Roslavets 185 List o-f Works by Genre 191
Appendix B: T-Level Identities o-f Individual Harmonies in "I", Measures 6-8 196 GDjowy's Analysis o-f T-Levels in "III" 198 An Analytical Alternative: A Single ICC •for "I", "II", and "III" 201 Prolongation o-f T-Levels.. 202 vii
LIST OF EXAMPLES AND FIGURES
Example 2-1. Pitch collections in "I", m. 1, and corresponding PCC T-levels 17
Example 2-2. Transposable PCCs o-f "I", "II", and "III", as illustrated by Perle, with numbering o-f PCs added 19
Example 2-3. ICC o-f "I", with T-level successions 23
Example 2-4. PC collection o-f m. 13 in " I" 26
Example 2-5. Expanded ICC and T-levels in mm. 6-8 28
Example 2-6. Expanded ICC at T-0 and its relationship to other PC collections in "I" and "II" 29 Example 2-7. ICC o-f "II", with PCs partitioned into
harmonies .31
Example 2-8. The ICCs o-f "III" 35
Example 2-9. Musical orthography o-f the ICC o-f "III" 41
Example 2-10. PC collections, m. 3 41
Example 2-11. Element "3" in mm. 3-4 42
Example 2-12. T-O collection, m. 12, as an inversion o-f ICC at T-0 .43 Figure 2-1. Transpositional relationships between successive T-levels in "I", "II", and "III" 45
Figure 2-2. T-level successions o-f "I" and the IC cycles 48
Figure 2-3. T-level successions o-f "II" and the interval 5 cycle 51
Figure 2-4. T-level successions o-f "III" and
the IC cycles 52
Example 2-13. Harmonic rhythm and -form o-f "I" 55
Example 2-14. Harmonic rhythm and -form o-f "II" ...58
Example 2-15. Harmonic rhythm and -form o-f "III" 60 v i i i
Figure 2-5. Hierarchy o-f T-levels based on -frequency o-f occurrence and total time-spans.... 62
Figure 2-6. Recurring T-level successions in Trois Compos i t i ons. 68
Example 2-16. Invariant PCs o-f IC-i- to IC-6- related T-levels 72
Example 2-17. PC invariance and pitch continuity in T-level successions of Trois Compositions .76
Example 2-18. PC invariance in IC-3-related T-level families..... 87
Figure 2-7. Successions of T-level families 88
Example 2-19. Primary melody of ' " I " 91
Example 2-20. Primary melody of "II".. 93
Example 2-21. Primary melody of "III" 94
Example 2-22. Harmonies of "I" with pitches represented by element numbers. 96 Figure 2-8. Element occurrences in vertical positions of the harmonies of "I" 98
Example 2-23. Harmonies of "II" with pitches represented by element numbers. lOO
Example 2-24. Harmonies of "III" with pitches represented by element numbers 102
Figure 2-9. Vertical element occurrence in ranges of positions in Trois Compositions. 105
Example 2-25. Similarities o-f harmonies in "I" (with pitches represented by element numbers)...... 106
Example 2-26. Similarities of harmonies in "II" (with pitches represented by element numbers) 108
Example 2-27. Similarities of harmonies in "III" (with pitches represented by element numbers)...... 111
Example 2-28. Similarities of vertical element orderings of harmonies in " I and "III" 113
Example 3-1. ICC T-levels T-0, T-li, and T-4 in "I" 127 ix
Example 3-2. Surface structures and progressions o-f Eb, D, and G tonalities in " I" 128
Example 3-3. Tritone sequences o-f mm. 6-8 and
their tonal implications.... 130
Example 3-4. Initiating single pitches in "I". 132
Example 3-5. Linear structures in "I" .134
Example 3-6. Melodic -fragments o-f mm. 1-5
and 10-13 o-f " I " 136
Example 3-7. The PC progression G-G*t/Ab in mm. 6-8...... 137
Example 3-8. Bass-line structures o-f "I" 138
Example 3-9. Midd1eground/background harmonic
structure o-f " I " 140
Example 3-10. ICC o-f "II" and its resemblance to F 141
Example 3-11. T-O harmonies in mm. 13, 1, and 10-12. .... 142
Example 3-12. Surface tonal -features in "II" 143
Example 3-13. Harmonies o-f mm. 6-9 and their tonal
imp 1 i cat ions.... 145
Example 3-14. Eb in mm. 3-5 145
Example 3-15. Arpeggiated diminished-seventh harmonies in the primary melody o-f mm. 6-9 147 Example 3-16. Midd1eground/background linear structures o-f "II" 149 Example 3-17. Midd1eground/background harmonic
structures o-f "II" 150
Example 3-18. The ICC o-f "III" 151
Example 3-19. Surface tonal structures in "III" 152 Example 3-20. IC-5-related PC successions in mm. 3-7 of "III" 153 Example 3-21. Midd1eground/background linear
structures of "III" 154
Example 3-22. F#/Gb and the linear structures of "III"..155
Example 3-23. Bass-line structure in "III" 156 X
Example 3-24. Midd1eground/background harmonic structures o-f "III" 158
Example 4-1. ICCs o-f Trois Compositions compared with octatonic col lections 166
Figure 4-1. Serial ordering o-f T-levels in Trois Compositions .170
Example 4-2. Serial ordering o-f primary melody and bass-line PCs 172
Example 6-1. Collections in mm. 6-8 and the most simi lar T-levels 196
Figure 6-1. T-level successions in "III", as given in Gojowy's analysis...... 199
Figure 6-2. ICCs "a" and "d" in "III" 200
Example 6-2. Prolonged T-levels in Trois Compositions... 203 ACKNOWLEDGEMENTS
I wish to extend my appreciation to the -following people:
Prof. Wallace Berry, my thesis advisor, -for his guidance, valu• able criticisms, and encouragement; Prof. William Benjamin, with whom I first began the thesis research, for his help and contin• uing interest; Prof. John Roeder, for reading the thesis and
giving valuable criticisms; Dr. Detlef Gojowy, for providing in• formation on current research into Roslavets; pianist Sarah
Rothenberg of New York, who graciously provided me with a tape
recording of a concert at New York's The Kitchen which featured premiere performances of works by Roslavets, including Trois
Compositions pour piano, with Ms. Rothenberg, violinist
Guillermo Figueroa, and cellist Jerry Grossman; Prof. Marketa
Goetz-Stankiewicz, for her assistance with German translations;
Prof. Barbara Heldt, for her assistance with transliterations of
Russian names; staff members of the Music Library and Inter-
library Loan Service; and family and friends in Vancouver and
Ontario, for their help and encouragement. Finally, I would
especially like to thank my wife Francine, whose assistance and
loving support have helped me to complete the thesis.
Excerpts from the score are used with the permission of
Music Associates of America, representatives for Boe1ke-Bomart,
Inc., copyright owners of Trois Compositions. 1 CHAPTER ONE
INTRODUCTION
At the beginning of this century, Russian art was in the vanguard of European development and it continued to be so well into the Soviet period. The Stalinization of Soviet music and the subsequent in• sistence on a national and popular symphonic style have served to obscure the work and the very exist• ence of an important and original group of Russian composers active in the first quarter of the century, including the remarkable Nikolay Rosslavetz [Nikolai Roslavets] (1881-1944), who anticipated aspects of twelve-tone music. . . .1
Although, from an historical perspective, Roslavets may be described as a "minor experimentator," he is, nonetheless, one of the more significant but little-known figures of avant-garde music in Russia during the first three decades of this century.
Biographical Information"
Born in the Chernigov region of the Ukraine, January 5,
1881, Roslavets came from a rural background. Saminsky finds i
"curious" that Roslavets, a sophisticated musician and thinker,
"should be a peasant pur sang, his parents being former serfs and he himself a shepherd boy up to the age of twelve.""*
Roslavets was initially self-taught in music. He himself indi• cates that his musical talent appeared around the age of seven or eight, and was manifested under the influence of his uncle, with whom he studied the violin. Later, Roslavets had lessons in Konotop, and eventually was admitted to the music classes of 2
A. M. Abaza, in Kursk, where he studied the violin, elementary theory, and harmony.0
From 1902 to 1912 he was a student at the Moscow Conserva• tory, studying violin with Jan Hrimaly CIvan Grzhimali (1844-
1915)3, counterpoint, fugue, and -form with Alexander A.
Il'inskii (1859-1920); and composition and orchestration with
Sergei N. Vasilenko (1872-1956). He graduated in 1912 with a silver medal for his cantata Heaven and Earth, based on the text by Byron. There are indications o-f his radical views while he was a student at the Conservatory."* However, there seems to be little information available concerning the composer's post-
Conservatory life and musical activities up to the early 1920s.
What is known about this period, largely through his autobio• graphical article, is his development of a new system of tonal organization.5'
In 1922, he was the temporary director of the Khar'kov Con• servatory.* He then worked on the editorial staff of the Moscow
State Music Publishing House, notably as the editor of and con• tributor to the Marxist and progressive periodical Muzykal'nara
Aul'tura (1924). (Only three issues of the journal were pub• lished.) Roslavets was generally quite active in the 1920s as a critic and writer on music, venting "his radical ideas in vari• ous essays in the mid-twenties, ... [which] earned him the en• mity of virtually everybody except a small group of extreme mod• ernists, "T One group with which he came into conflict was the more conventionally oriented Association of Proletarian Musi• cians Clater, Russian Association of Proletarian Musicians, or 3
RAPM3, which "reproached him -for his bourgeois ideology."*-0
Until 1929, he was a board member of the modernist Association
•for Contemporary Music, the Soviet association closely linked with ICSM. In 1928-29, ACM was reorganized as the All-Russian
Society -for Contemporary Music, but it ceased to exist by
1931. 11 In the latter half o-f the 1920s, the limited response
to his works, and pressure -from RAPM and Soviet authorities led
him to abandon his avant-garde style of composition -for a more
acceptable tonal style. Roslavets publicly confessed his previ•
ous errors (i.e., "his modernist style and his avoidance of the
emotional") in 1930 in the Proletarian Musician LProletarsk i i
Muzykant, journal of RAPM 3.12
Roslavets "then accepted an invitation to Tashkent tin Uz•
bekistan, a region of the Soviet Union] where he switched to
folk music in Uzbek style and composed the first national Uzbek
opera. All music dictionaries published in the West speculate
that Roslavetz was banished from Moscow and that he disappeared
without trace in the wake of the political purges of the 1930s.
Perhaps he moved to Tashkent to escape political reprisals."1"
More recently however, Gojowy has provided little-known informa•
tion about Roslavets and his activities after the 1920s, dismis•
sing rumours about Roslavets's exile to and death in Siberia
that arose as a consequence of his "non-person" status under the
cultural policies of Stalin and Zhdanov.14
Roslavets went to Uzbekistan in 1931, where he became one of the first Russian musicians to contribute to the development of musical culture in Middle Asia. He was director of the Radio Center of the Uzbek So• viet Republic and conductor of the Uzbek Music The• ater. He composed music based on [Uzbek] national 4
melodies and rhythms. His ballet Pakhta ["Cotton peasant"], dedicated to the struggle for independence o-f the cotton industry in the USSR, and his symphony, "Soviet Uzbekistan," composed -for the 15th anniversa• ry o-f the October Revolution, were performed with great success under his baton. He was awarded an honorary diploma by the government of the Uzbek Republie. In November 1933, he returned to Moscow as a producer for the All-Union Radio Committee (1933-35) and as director of the All-Russian Concert Associa• tion (until 1939); from 1936, he served as head of the section of scientific collaborators in the trade union RABIS. He taught composition in the Musical Po1ytechnical School, lectured to military band di• rectors, and continued to compose. During these years he wrote important theoretical works, such as "Counterpoint" and "Fugue," which remain unpublished. Although he was seriously ill during the Second World War, he became intensely involved in the general struggle and composed patriotic songs dedicated to the defenders of his country. . . .ie »
Roslavets died in Moscow, August 23, 1944.
Aspects of Roslavets's Compositional Style and Technique
Roslavets's student compositions and earlier chamber works were influenced by French impressionism.1"* But soon after the completion of his studies, his style changed. In the 1910s,
Roslavets developed a series of harmonic principles of a new to• nality, applicable to his music. He indicates having a vague notion of these principles, even finding them to be evident in his student compositions of 1909-1911. In early 1913, he com• posed the first works, a violin sonata and some songs, which manifested his own individual ,compositional techniques, and for the next six years, until 1919, he continued to develop these techniques.17 Gojowy cites the songs Volkovo kladbishche (text by Burliuk) and Vy nosits liubov' (Bo1'shakov), both from the end of 1913, as pieces in which Roslavets "achieved a new har- 5 manic ordering which w'as nat diatonic and which he referred to
as the synthetic chord technique."10 These chords, the basis of
the harmonic organization in his music, consist of six to eight and more pitches, are transposable to all twelve chromatic lev•
els, and can include tertian chords o-f conventional tonality.
Such "synthetic" chords are used not only -for colouristic pur• poses but, more importantly, to substitute for conventional ton• al structures. Although the principle o-f classical tonality is absent -from Roslavets's works up to the time of his autobio•
graphical article (1924), "tonality as a concept of harmonic unity exists unchanged and appears in the form o-f the aforemen•
tioned synthetic chords. . . . "1» These chords can be expressed vertically or horizontally, and involve some rules of voice-
leading.20 In addition, principles of "a new polyphony," and
"new rhythmic forms" were developed, so that, by the end of
1919, he came to a fuller awareness of all these principles as
elements of a "new system of sound organization." This system,
in his opinion, was "destined to ultimately replace that of the obsolete classical system . . . and to lay a firm foundation un•
der the intuitive (in fact, only anarchistic) compositional methods with which the majority of contemporary composers opera-
teCdl. . .
In general, Roslavets's music is characterized by a number of different influences and trends. The noted Russian musicolo•
gist, Boris Asafiev, discusses one of these:
Somewhat apart, in view of its sharp antagonism to contemporary currents, stood the output of Roslavetz. . . . As is demonstrated by the first vio• lin sonata (1913), and then by a number of other 6
works, Roslavetz already then set up, in a far-sight• ed and daring manner, the problem o-f constructivism that we are at present so much concerned with. It was necessary to speak o-f his works at that time us• ing a terminology that has now become elementary, as: the organizational principle, a strictly constructive system, and a business-like accuracy in mastering the material. Roslavetz was, and has remained quite aloof from modernism. Though he used a different type of material, Roslavetz fundamentally sought the same as Schoenberg --the precise laws of a severe logic of sounds. Roslavetz realized that true classicism does not lie in safeguarding the methods of the "old men" and not in a stylization of modern music with their methods and by using archaic material, but that the question is of elaborating a strict system of sound-organiza• tion, whence will naturally -follow classically per• fect compositions, through a formation of new materi• al.22
"Constructivism" was a
Russian artistic and architectural movement that was first influenced by Cubism and Futurism and is gener• ally considered to have been initiated in 1913 with the "painting reliefs"—abstract geometric construc• tions— of Vladimir Tat 1in. Antoine Pevsner and Naum Gabo joined Tatlin and his followers in Moscow, and upon publication of their jointly written Realist Manifesto in 1920 they became the spokesmen of the movement. It is from the manifesto that the name Constructivism was derived; one of the directives was "to construct" art. Because of their admiration for machines and technology, Functionalism, and modern industrial materials such as plastic, steel, and glass, they were also called artist-engineers. Soviet opposition to the Construetivists' aesthetic radicalism resulted in the group's dispersion.23
Roslavets's development of a new system of pitch and pitch- class organization, and the "anti-emotionalism and formalism"2"*
that characterized his work, would seem to represent in part a musical manifestation of constructivism.20
Just as significant are references in a number of sources
to the composer as a "Russian Schoenberg" and as a "Scriabin-
ist. " Roslavets denies that his system is influenced by 7
Scriabin, or by Schoenberg, although he admits "Skryabin (in a musical-formal respect, but in no wise ideologically . . .) is of course -far nearer to me than Schoenberg, whose work, I con• fess, I have got to know only comparatively recently."2* There are in fact indications of limited contact between Scriabin and
Roslavets:
N. A. Roslavets is regarded as a strong follower of Scriabin. ... Indeed, he [Roslavets] considered Scriabin as his most important teacher. Apart from the fact that Roslavets frequently submitted his works to Scriabin, there was no direct contact be• tween the two. It is known that Scriabin considered Roslavets's atonal works favourably, particularly the first Sonata for Violin and Piano (1913). During this period, Roslavets formulated his ideas in the theoretical work Navaya si sterna organ i zac i i zvuMov CA New System of Sound Organization], Roslavets here based his theory on the works of Scriabin; likewise this thesis also contains consideration of the works of A. Schoenberg. Roslavets observed with Scriabin certain sound complexes and described them as "syn• thetic chords." This theory of "sound complexes" found their practical application in a series of sym• phonic and chamber music works by Roslavets of the period from 1919 to 1924.^
However, according to Schwarz, Roslavets's Violin Sonata
(1913) was the first atonal work by a Russian composer, and his
String Quartet No. 3 of 1920 employed a "tone row" technique.28
In fact, there are a number of similarities between the composi•
tional technique of Roslavets with that of Schoenberg:
[Roslavets] developed the ["synthetic chord"] technique in piano miniatures, so that by 1915 it had become a 12-note system, embracing concepts of 12- note serial ism and mirror symmetry. In the Violin Concerto (1925) he added the principle of complemen• tary pitch-class groups which together form 12-note sets. His sensitive, consistent 12-note writing has many similarities with that of Schoenberg, whose work, however, Roslavets did not encounter until 1923.
Roslavets's works "found only limited response. Even- 3 tually, he seemed to relent in his doctrinaire approach."30
Roslavets's style changed to a more accessible tonal style.
Roslavyets's CRoslavets's] Marxism and his asso• ciation with communistic theories and practice could not fail to affect his compositions. He considered it his duty to come out as composer of revolutionary music. Beginning with 1913, revolutionary music in Russia was created in bulk and poorly, and in accor• dance with specifications and requests from the res• pective organisations. Roslavyets was the first "convinced" composer of music for the proletariat. He set himself the task of eradicating the dilettan• tism from composition of this kind and their invari• ably poor style and taste, usually derived from the repertory of the operetta and "light" music. Even for the proletariat Roslavyets endeavoured to write masterly and complex music. But in spite of his theoretic premises that the most complex music is within the grasp of the workingman, if it but "orga• nises tonal matter" well, Roslavyets finally had to make a number of concessions, and his revolutionary compositions, written for workmen's clubs, differ strongly in style from his "serious" compositions. Everything is simpler, more primitive and his usual complex musical language (the modernistic one) gives way to a plainer one. As an intermediate essay, Roslavyets wrote several songs to revolutionary texts by present-day Russian poets and some of bygone years, preserving his style intact. Such are Songs of the Labouring Professions, and The Songs of the Pevolutionr two volumes which cannot be denied their structural musical merits."1
Roslavets's style in the cantata October (1924) was described as
"somewhat too sentimental" and "reminiscent of Strauss and
Wagner. "3SB
Schwarz mentions that, in the 1930s, Roslavets wrote
lighter theatre music, as well as compositions based on -folk, especially Uzbek, music.33 In addition, Roslavets wrote agita• tion-propaganda music, and, as suggested by Gojowy*s recent
listings of pieces by the composer (see Appendix A), classical tonal compositions in the 1930s and 1940s.3"*
Considering these observations, one might tentatively 9
identify four periods in Roslavets's compositional career, namely: (1) an early, student period, up to 1912; (2) 1912-
1919, a post-Conservatory or development period in which his compositional technique was developing; (3) 1919-1925, a mature period that includes both polyphonic styles (involving linear expressions of tone complexes) and, especially towards 1925, more Romantic styles (e.g., use of Tristan harmonies);3* and (4)
1925-1944, a period of tonal compositions, including the writing of agitation-propaganda songs and music based on folk songs.
Trois Compositions pour piano (1914) represents the compos• er's development of compositional technique in the second, post-
Conservatory phase of his career. Roslavets developed his syn• thetic chord technique in piano miniatures, such as Trois Compo- sitionsi in fact, the first two pieces of the set involve a strict application of the technique whereby one "synthetic chord" or pitch-class complex (PCC) determines the harmonic structures of a piece. Moreover, such pieces, especially those composed towards 1915, exhibit certain features of twelve-tone ser ialism.3d
Gojowy's Neue sowjetiscfte Musi A der 20er Ja/>re, and his numerous articles on Russian musical developments, including those dealing specifically with Roslavets,3" present the most detailed published studies of the composer's life and works to date; the former includes an analysis of Trois Compositions.
George Perle's brief analytical discussion of the three pieces
in Serial Composition and Atonality represents one of the first
English-language analyses of Roslavets's music.30 IO
Although Gojowy and Perle together identi-fy such aspects o-f
Trois Compositions as PCCs associated with the pieces, transpo• sition levels o-f these PCCs (which -form the bases o-f harmonic units), and general characteristics of Roslavets's style, few details concerning pitch-class (PC) and pitch organization in the pieces are provided. Hence, the primary objective of the present thesis is a comprehensive investigation of PC and pitch organization, beyond what has been treated elsewhere. Chapter
Two will deal exclusively with the "synthetic chord" technique, presenting the observations of Gojowy and Perle as a basis for further analytical studies. Harmonic successions, their PC content, and the ordering of PCs within individual "synthetic chords" will also be examined in some detail. Chapter Three will deal with tonality as that concept applies to Roslavets's organization of PCs and pitches, and Chapter Four will treat aspects of octatonic and serial organization that apply to the music.
Notes
1. Eric Salzman, Twentieth-Century Music: An Introduction, 2nd ed. (Englewood Cliffs, New Jersey: Prentice-Hall, 1974), 27-28. Similarly, Jim Samson indicates the significance of Roslavets: "The importance of Russia as a centre for progres• sive thinking in the arts at the turn of the century has only recently been fully appreciated. . . . The atonal Violin Sonata and proto-serial Three Piano Pieces of Rosslavetz [Roslavets], both dating from 1913-14, and the mechanistic compositions of Mossolov CMosolov] and Desschevov CDeshevovl in the twenties help to place in some sort of perspective the second decade achievements of Stravinsky and Prokofiev. (Jim Samson, Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920 [London: J. M. Dent and Son, 19773, 73-74.)
2. The description of "minor experimentator" is found in Boris Schwarz, Music and Musical Life in Soviet Pussia: Enlarged 11
Edition 1917-1981, 2nd, enlarged ed. (Bloomington, Indiana: Indiana University Press, 1983), 9 (hereafter cited as Mus. Soviet Puss i a) .
3. Information in this chapter on Roslavets is taken from the following authors (see bibliography -for additional informa• tion): Nikolai Roslavets, Detlef Gojowy, Lazare Saminsky, and Leonid L. Sabaneyeff CSabaneev]. Encyclopaedic sources include: New Grove Dictionary of Music and Musicians, 6th ed., s.v. "Roslavets" (hereafter cited as Grove, 6th ed.)J Die Musik in Geschichte und Gegenwart, s.v. "Ros1awetz" (hereafter cited as MGG); Das Grosse Lexikon der Musik, s.v. "Ross1awetz"i and Baker's Biographical Dictionary of Musicians, 7th ed., s.v. "Roslavetz".
4. Lazare Saminsky, Music of Our Day: Essentials and Prophecies (New York: International Publishers, 19275 New York: Da Capo, 1975), 264. Concerning the date of birth, some sources indicate the Julian calendar date (i.e., December 24, 1880). Curiously, Das Grosse lexikon der Musik indicates January 4, 1881 (December 23, 1880, Julian calendar) as the date of birth. {Das Grosse Lexikon der Musik, s.v. "Ross 1awetz) Roslavets mentions that he was born in the village of Dushatino, and later- lived and worked in Konotop, both communities in the former gov• ernment district of Chernigov in the Ukraine. (Roslavets, "Nik. A. Roslavets o sebe i svoern tvorchestve," CNik. A. Roslavets on Himself and His Work], Sovremennaia muzyka CContemporary Music], 5 C1924]: 132-133 Ctrans. in Gojowy, Neue sowjetische Musik der 20er Jahre (Laaber: Laaber-Ver1ag, 1980), 395; hereafter cited as "Ros1avets"-NsM.]) Apparently, Dushatino was renamed Surazh, now part of the Briansk Oblast [region!, based on information in Piemann Musiklexikon: £rganzungsband, 1975 ed., s.v. "Ross 1awets", and in Das Grosse Lex ik on der Musik, s.v. "Rosslawets".
5. Roslavets, "Ros1avets"-NsM, 395.
6. Saminsky echoes Roslavets in indicating that, "while at the conservatory he [Roslavets] was disliked for radicalism ." and that once he -finished his studies, he "rid himself of the conservatory prescriptions very quickly." (Saminsky, Music of Our Day, 264; see also Roslavets, "RosIavets"-NsM, 396.)
7. Roslavets, "Ros1avets"-NsM, 396-393.
8. Gojowy's indication that a cello sonata was composed in Khar'kov, in March of 1921, suggests that Roslavets was living in or near the town before his directorship. (Gojowy, "Nikolaj Andreevic Roslavec, ein f rCiher 2w6 1 f tonkompon i st, " Die Musik- forschung, 22/1 [January-March 19691: 37.) Interestingly, one source provides information on the founding in 1922 of a school of composers at the Khar'kov Musical Institute (later the con• servatory) by S. Bogatiryov, although there is no mention of Roslavets. (Grove, 6th ed., s.v. "Khar'kov".) 12
9. Schwarz, Mus. Soviet Russia, 86. Among his accomplish• ments was the first Russian introduction to Schoenberg's Pierrot Luna ire. ("Lunnly P'yero Arnol'da Shyonberga," K novim beregam 3 [19233: 28; reference in Swe, 6th ed. , s.v. "Roslavets".)
10. Grove, ibid.
11. "[The3 ACM's journal Sovremennaia Muzyka ceased publi• cation in March 1929, followed in 1930 by the demise of the ex• cellent monthly Muzykal'noye Obrazovanie which had represented the independent musical intelligentsia and the conservatory circles. Only the brash voice of Pro letarsk i i fiuzyk ant [journal of RAPM3 was left, pretending to speak for all the musicians. In the meantime, many important members had abandoned the ACM, among them Miaskovsky, and the organization simply ceased to function even prior to its dissolution in 1931." (Schwarz, Mus. Soviet Russia, 58-59.)
12. Percy A. Scholes, ed., The Oxford Companion to Music, 9th ed. (New York, Toronto: Oxford University Press, 1955), 895. Roslavets, in his autobiographical article ("Roslavets"- NsM, 398), argued his aesthetical position using "a Marxist defence of an aesthetic of musical positivism, which opposed the idea of an objectively definable emotional quality and which saw the creative act as a moment of the human intellect's highest exertion, looking forward to the subconscious being realized in the form of the conscious and to music based on a new fixed system of tone organization." (Gojowy, Grove, 6th ed., s.v. "Roslavets".)
13. Schwarz, Mus. Soviet Russia, 86. There are no indica• tions in the literature to date that Roslavets in fact wrote an opera, much less the first national Uzbek opera. Curiously, his former composition and orchestration teacher, Sergei Vasilenko, in collaboration with Uzbek composer M. Ashrafi, is credited with this accomplishment: "In 1938 he [vasilenko] worked in Tashkent on the first Uzbek opera, Burian [The Snowstorm3." (Grove, 6th ed., s.v. "Vasilenko.")
14. One such "unconfirmed report" about the death of Roslavets in Siberia is given in MGG, s.v. "Rosiawetz".
15. Gojowy, "Half Time for Nikolai Roslavets (1881-1944): A Non-Love Story with a Post-Romantic Composer," Russian and Soviet Music: Essays for Boris Schwarz, ed. Malcolm Hamrick Brown (Ann Arbor, Michigan: University Microfilms International Research Press, 1984), 215-216; quotation from In the World of Music [V mire muzyki3, (Moscow, 1981): 5. Gojowy also refers to another source concerning the activities of Roslavets in the 1930s. iMuzyka I'naia entsiklopediia, [Moscow, 19783, s.v. "Roslavets" [vol. 4, cols. 711-7123.)
16. Grove, 6th ed., s.v. "Roslavets". Interestingly, 13
Montagu Montagu-Nathan states that Roslavets had been "influ• enced a little by Rebikof. ..." (Montagu Montagu-Nathan, Con• temporary Russian Composers [London: Cecil Palmer and Hayward, 1917; Westport, Connecticut: Greenwood, 19703, 315.) Vladimir Ivanovich Rebikov (1866-1920), Russian composer, developed a style o-f composition that employed the whole-tone scale and augmented triad, and "claimed priority in this respect over Debussy and other European composers." (Baker's Biographical Dictionary of Musicians, 7th.ed., s.v. "Rebikov".) This "earned him a reputation as the -finest Russian impressionist, and he also became known as the -father o-f Russian modernism." (Grove, 6th ed., s.v. "Rebikov".)
17. Roslavets, "Ros1avets"-NsM, 396-398.
18. Grove, 6th ed., s.v. "Roslavets".
19. Roslavets, "Roslavet5"-/Vs/>i 396-397. The reference to "pitch" is clarified in Chapter Two with discussion of the term "pitch-class" (PC).
20. Ibid., 397. Saminsky states: "From his harmonic foun• dation he evolved several years ago a peculiar system of voice leading and a new polyphony which led to his tonal organiza- tion." (Saminsky, Music of Our Day, 265.)
21. Roslavets, "Ros 1 avets "-/V^/9, 397.
22. Boris Asafiev, Russian Music from the Beg inn ing of the Nineteenth Century, trans. Alfred J. Swan (Ann Arbor, Michigan:. J. W. Edwards, 1953): 262.
23. The New Encyclopaedia Britannica, 15th ed., s.v. "Constructivism". Interestingly, M. Montagu-Nathan indicates Roslavets's interest in artistic aspects associated with the movement: "Roslavets is a versatile composer and evidently a man of cultivated tastes and wide sympathies. . . . As to exter• nal symptoms it is worthy of mention that Roslavets affects col• oured ink, a circumstance which will have some significance for students.of latter-day tendencies; more striking than this are the Cubist designs which adorn the covers of some of his pieces." (Montagu Montagu-Nathan, Contemporary Russian Composers, 315.)
24. Leonid Sabaneyeff [Sabaneevl, Modern Russian Composers, trans. Judah Jaffe (New York: International Publishers, 1927; Da Capo, 1975), 203.
25. The "fad of such constructivist music became very popu• lar in the later 1920s, but none was as highly acclaimed as Mosolov's Iron Foundry, called a mighty hymn to machine work by one Soviet critic, a symbol of the enthusiasm of Socialist in• dustrialization." (Schwarz, Mus. Soviet Russia, 85; quotation from Is tori a Muzyki Narodov SSSR, [Moscow, 1966 3, vol. 1, p. 14
169.) Gerald Abraham likewise refers to Roslavets as an anti- romantic constructivist. (Abraham, "The Reaction Against Roman• ticism: 1890-1914," New Ox ford History of Music, ed. Martin Cooper [Toronto: Oxford University Press, 19743, vol. 10, p. 137. )
26. Abraham, ibid.
27. Michael Goldstein, "Skrjabin und die Skrjabinisten. Das Schaffen Skrjabins und seiner Nachfo1ger—Induktion und Deduktion," Musik Konxepte 32/33. A left sand r Skrjabin und die Skrjabinisten, ed. Heinz-Klaus Metzger and Rainer Riehn, trans, of article from Russian to German by P. Ruhl (Munich: Edition Text + Kritik, 1983), vol. 32-33 (September 1983): 181 (my translation). Goldstein also includes a short analysis of Roslavets's Uetre nalet i te (1913; text by A. Blok) on p. 188. Other sources indicate Roslavets's association with Scriabin; for example, Sigfried Schibli includes Roslavets in "a close circle of Scriabinists." (Sigfried Schibli, Alexander Skrjabin und seine Musik. Grenxuberschreitungen eines prometheischen Geistes. [Munich, Zurich: R. Piper and Co. Verlag, 19833, 348; my translation.)
28. Schwarz, Mus. Soviet Russia, 86.
29. Grove, 6th ed., s.v. "Roslavets".
30. Schwarz, Mus. Soviet Russia, 86.
31. Sabaneev, Modern Russian Composers, 206-207.
32. Schwarz, Mus. Soviet Russia, 86; quotation from E. Braudo, fl/'e Musik, 20/7 (April 1928): S3. Although Schwarz in• dicates 1927 as the date for October, it was actually composed in 1924.
33. Schwarz, /?us. Soviet Russia, 86.
34. Gojowy, "Half Time," 217-219.
35. Gojowy states: "Around 1920 (Third Quartet, Medita• tion), he again changes from the polyphony and contrapuntal forms to a milder Tristan harmony with the Violin Concerto (1925)." (Gojowy, Neue sowjetische Musik, 985 my translation.)
36. Grove, 6th ed., s.v. "Roslavets"; Gojowy, Neue sowjetische Musik, 138.
37. Gojowy, "Roslavec," Die Musikforschung, 22/1 (1969): 22-38, and "Half Time," 211-220.
38. George Perle, Serial Composition and Atonality, 4th rev. ed. (Berkeley, Los Angeles: University of California Press, 1977), 43-44. I 5"
CHAPTER TWO
THE INTERVAL-CLASS COMPLEX IN TROIS COMPOSITIONS
Introduction and Terminology
As the analyses by Detlef Gojowy and George Perle are pioneering studies o-f the work a-f Roslavets, we turn initially
to them -for preliminary insights into Trois Compositions, with which they both deal.
The compositional system o-f most early works by Roslavets is based on the principle o-f transposable tone complexes in scale -form that represent the en• tire tone collection in a given time-span. A given tone complex determines which tone need or need not sound, although not in which order, oc• tave, or motive. Within the chromatic scale, there are eleven possible transposition levels -for every possible complex. This system was not invented and utilized exclu• sively by N. A. Roslavets, but indeed, i-f one be• lieves his own testimony, was developed independently o-f Scriabin's similar system.1
More recently, Gojowy states:
[Roslavets's system] was based on chords o-f six to eight or more tones, used . . . as substitutes -for the -functional relationships o-f classical tonality, which he did not reject but tried to expand. These "synthetic chords" o-f specific and invariable inter• val lie structure could be transposed . . . to all twelve degrees o-f the chromatic scale. . . . tin] the tone complex, as used by Scriabin and Roslavets, the order o-f its elements remains -free; the complex is de-fined only by its intervallic structure.2
More specifically, Gojowy's analysis identifies the "transpos•
able tone complexes" associated with the three pieces, and the
transposition levels (T-levels) of each complex from which pitch 16 collections in the respective pieces are derived.
Perle's study in Serial Composition and Atonali ty includes a listing in musical notation of the "sets" or transposable tone complexes associated with each piece, an analysis o-f the PC con• tent o-f a short excerpt o-f "III" and identification of tone com• plex T-levels, and a brief description of the salient points of
Ros1avets's compositional technique, part of which is quoted below:
In his Trois Compositions for piano, Roslavetz employs an independent set for each move• ment. . . . As in Scriabin's works, the set functions simultaneously as scale and chord. Transpositions are used much more freely, pivotal connections being employed, in general, merely as a means of immediate assoc i at i on.3
To begin, some clarification and additional terminology is required to facilitate further analysis. The "transposable tone complex," an important aspect of pitch and pitch-class (PC) or• ganization in Roslavets's music, is designated by the different authors as "synthetic chord" (Roslavets), "Tonkomplex" (Gojowy), and "set" . (Per le) . Specifically, it involves a collection of pitch-classes (PCs) and hence is more accurately termed a
"pitch-class complex" (PCC).° To understand how PCCs are trans• posed and employed in the music, Ex. 2-la illustrates m. 1 of
"I", with the pitches segmented into collections. These collec• tions can be tentatively designated as harmonies, given the si• multaneous occurrences of pitches involved and generally verti• cal orientation of pitches in most collections.'* In Ex. 2-lb, the pitch-classes (PCs) represented in the collections of Ex.
2-la are ordered to illustrate similarity of PC collections 17 v through transposition. Each ordered PC is numbered according to the PC interval it -forms with the -first PC o-f the collection.
Example 2-1. Pitch collections in "I", m. 1, and corresponding PCC T-levels.
(a)Pitch collections in "I", m. 1:
(b) T-O T-3 T-10
0 13468 910 0134689 0134689
INTERVAL VECTOR: 14 S 6 S 3 31 13 3 3 4 4 21 13 3 3 4 4 2)
Segmentation o-f pitches into collections in order to iden•
tify the PCC T-levels, as shown in Ex. 2-1, is partially indica•
ted in Gojowy's analysis o-f Trois Compositions which includes
the successions o-f PCC T-levels (and measure indications).
Moreover, both Perle and Gojowy indicate the transposable PCCs
associated with each piece.'' But, segmentation o-f pitches into collections is a relatively simple matter anyhow, given the gen•
erally homophonic texture o+ the pieces, with many o-f the col•
lections appearing as simultaneities or recognizable arpeggia-
tions thereof. More importantly however, the time-spans and
temporal placements of the pitch collections generally coincide 18 with the notated meter, in the sense that the initial attack- points of many harmonies correspond to the barline or to conven• tional time-points o-f metric subdivision within the bar (e.g., in 4/4 meter, time-spans initiated on the second, third, or fourth "beats")."
In Ex. 2-lb, the -first harmony in m. 1 o-f "I" is designated as T-O because it is the -first o-f the piece, the -first T-level o-f the PCC. More importantly, it is a referential harmony in the sense that, as later analyses will show, this PC collection begins and ends the piece (as do the initial PC collections of
"II" and "III", respectively), and, of any T-level of the PCC of
"I", it occurs most frequently and has the greatest total time- span .
Also in Ex. 2-lb, the listing of ordered PCs of each col• lection in m. 1, with PCs numbered according to the PC interval they -form with the first PC of each scale, illustrates how the second and third harmonies of m. 1 are transpositional1y related to the first, in terms of PC content, with one minor exception
(i.e., C in T-0 not being transposed in T-3 and T-10). In addi• tion, the interval vectors" of the three harmonies are indica• ted, to illustrate that T-O is similar to a limited extent in interval-class (IC)10 content to T-3 and to T-10, while T-3 and
T-10 have the same IC content.
The particular ordering of T-O PCs, starting with D, is based in part on Perle's presentation of PCCs for each piece
(each at T-O), shown in Ex. 2-2 with ordered PCs numbered as in
Ex. 2-lb. 19
Example 2-2. Transposable PCCs of " I " , "II", and "III", as illustrated by Perle, with numbering o-f PCs added.
PCC OF T, T-0:
0 1 3 4 8 9 (101
PCC OF •ii*, T-O: V
0 (1) 3 4 8 9 11
PCC OF -in-, T-O:
0 1 3 4 8 (9) (10) tin
The bracketed PCs in each ordered collection represent those PCs or transpositions thereof not appearing with every T- level, an issue which will be -further investigated in the -fol• lowing section o-f this chapter. Given that the PCCs of "I" and
"III" are in the prime -form, when one excludes -from considera• tion the variant PCs, and given the similarities o-f the three transposable PCCs, D is the -first PC o-f the ordered PCC at T-0 for "I", and likewise C#/Db is the first for the PCC of "II", and G for the PCC of "III". Based on the PC numbering scheme illustrated in Exx. 2-1 and 2-2,11 any PC in a given T-level is designated with a number, an "element" number, in order to show its relationships to the other PCs of that T-level. One PC in nearly every T-level occurrence (i.e., collection in the music) will be designated with element number "O", although this does not imply any greater significance to this PC.*-2 Given that 20 certain elements do not appear in the PCCs (at T-O) as shown in
Ex. 2-2, these will likely not be represented in the pitch col•
lections of the pieces. O-f course, a PC which is a given ele• ment in one T-level cannot be the same element in another T-
1eve1.
Because the PCC as Roslavets uses it has a "specific and
invariable interval lie structure" which can "be transposed . . . to all twelve degrees of the chromatic scale,"43 such a PCC will be referred to in the thesis as an interval-c1 ass complex (ICC).
Such an ICC consists of an ensemble of ICs spanning the constit• uent PCs (as shown in Ex. 2-1 with the interval vector). For purposes of classification, component PCs are abstracted as an ascending scale. The IC relationships between PCs of a PCC nec• essarily remain the same when those PCs are assigned registral and temporal identities in the music.
A given ICC is transposable in the sense that the PCs that constitute it are transposable. In other words, an ICC may be realized by various PCCs. (It is understood that the operation of transposition does not apply to intervals or ICs.) T-levels are designated "T-x", "x" representing the number of semitones of transposition above the T-level of the referential PCC that begins and ends a given piece (T-O). Hence, the T-level is a simple way of indicating a harmony's PC content independent of specific temporal and registral location. With some exceptions, most if not all of a given T-level*s PCs appear in any given harmony in Trois Compositions. The temporal and registral or• dering of elements can and usually does vary with every harmony 21 or T-level. The designation in this thesis o-f a T-level in a given measure is used to refer to the PC collection o-f that T- level or harmony. It is often not necessary to be concerned with the temporal and registral configurations of PCs.
This chapter will provide more insight into Roslavets's ICC system, incorporating the analytical observations of Gojowy and
Perle as a basis for further detailed examination of composi• tional technique in the pieces. The first part of this chapter examines the ICCs of the three pieces and how the harmonic units are derived from these ICCs. The second part investigates har• monic successions and T-level occurrences, while the final sec• tions deal with T-levels as to PC content, and vertical and lin• ear element ordering within individual harmonies and in element successions involving adjacent harmonies. 22
The ICC in Trot's Compositions
Gojowy indicates that two o-f these three pieces are each based on a single transposable PCC that we consider to be a single ICC. The observations o-f Gojowy and Perle generally con• cur, with some minor exceptions. We can clarify the organiza• tion o-f the PC material in all three pieces by segmenting each piece into PC collections.
ICC o-f "I"
Perle and Gojowy cite the same PC collection as the basis
-for the harmonies o-f "I", except that Perle includes the brack• eted variant element "10" (i.e., C in T-O, as represented in Ex.
2-2). The bracketed PCs in Perle's ICCs are those elements not appearing with every T-level occurrence. He indicates that
"Cvlariants o-f the set are more or less consistently employed.
These are derived not through the chromatic inflection of set- elements, as in Scriabin's Seventh Sonata, but through the sys• tematic omission of certain components of the basic forma• tion. " 10
The ICC of "I" is presented in Ex. 2-3a, and the segmenta• tion of pitches into ICC T-levels (in scale form, with T-levels
indicated) in Ex. 2-3b.1«* 23
Example 2-3. ICC of* "I", with T-level successions.
(a)T-O PCCs o-f the ICC o-f "I":
n [no
ELEMENT: 01 34 6 89 10 0
(b)Pltches o-f "I" segmented into PCCs at various T-levels:
MEASURE: (1) 121 PITCHES:
A
2
SCALAR REPRESENTATION OF PCC: T-LEVEL: O 3 10 24
Example 2-3b continued.
(41 (31 (61 25
Example 2-3b continued.
(10,111 (12) [131
¥-
*f-—STV-
• 6 •
1 , Vr'*" r-— r~7zb* ffr*-—
Some harmonies contain pitches which cannot be understood as part o-f the PCC Gojowy describes: C5 (m. 1, T-O); B4 (m. 4,
T-ii); B5 (m. 7, T-ll); and Eb4 (m. 7, T-ll). Perle's variant element "IO" (C) in his version o-f the T-O PCC accounts -for all but the last o-f these anomalous pitches, Eb4 being element "2" which is not -found with any other T-level in "I". The element
"10" PCs in question have a subsidiary or elaborative function, although element "2" (Eb) is a significant bass-line pitch. On
the other hand, the locations of collections containing variant elements have a certain formal significance: T-O (m. 1) and T-
11 (an exact transposition of the T-O harmony, m. 4) initiate
the first and second phrases of the piece, respectively; and T-
11 (m. 7, different temporal-registral configuration of pitches
to the previous T-ll) precedes the time-span with the pitch- c1imax of the piece (G#6).
Another problematic PC collection is that of m. 13. Gojowy
identifies it as T-O; in fact, the PC content is nearly identi• cal to T-O, except that G appears instead of Gb. Perle speaks 26 of the pitch material as being derived -from "transpositions o-f the set [complex] that are closely related in pitch content to the original statement o-f the set."15* It is possible to identi• fy the collection as the ICC at T-9 as well as at T-0, since six o-f seven PCs belonging to either T-level. One plausible expla• nation involves its connective function with "II": the PC col•
lection in m. 13 is identical to the PCC of "II" at T-10 (Ex.
2-4) .
Example 2-4. PC collection of m. 13 in "I".
ICC of "I" at T-O:
ICC of "I" at T-9: oM4
PC Content of m. 13:
ICC of "II" at T-10:
T-level identification in mm. 6-8 is problematic because of fewer PCs per collection and because more than one T-level can
be adduced to explain the PC content of each collection.
Gojowy*s analysis of T-level succession (Ex. 2-3b) explains 27 these individual collections as "different, irregular scale- excerpts,"10 excerpts of the ICC at some T-level. Perle does not discuss these measures specifically. Example 2-5 illus• trates that each of the complete PC collections of the second halves of mm. 6 and 7, and of m. 8, are derived from an expanded version of the basic ICC, which differs from the above-mentioned expanded ICC realized in mm. 1, 4, and 7. Example 2-5, staff
(a), illustrates the PC content of the individual harmonies, while staff (b) shows these PCs combined into larger collections
(i.e., T-levels of the expanded ICC), both in scale form. These are compared with similar T-levels of the basic ICC of "I" on staff (c). 28
Example 2-5. Expanded ICC and T-levels in mm. 6-8.
161 (SECOND HALF) (7) (SECOND HALF) UIPC CONTENT
(b)EXPANDED ICC AI T-0 ...AT T-2
(c)BASIC ICC AT T-0 ...AT T-2 ...T-2 .AT T-9
(81 (a)PC CONTENT
^ 1 il 1 Jl f*'\
(b)EXPANDED ICC AT T-7
• j),*J»> 'W
IcIBASIC ICC AT T-7 ...AT T-2
2^
The expanded PCCs are transpositionally related, with the expanded PCC o-f m. 7, second half, T-2 o-f the expanded PCC o-f m.
6, second half, and the expanded PCC of m. 8 T-7 of the expanded
PCC of m. 6. The temporal-registral configuration of pitches in these three time-spans reflects this T-O,T-2,T-7 transpositional relationship of the expanded PCC (Ex. 2-3, mm. 6-8). The ex• panded T-0 (m. 6) closely resembles the basic ICC of "I" both at
T-O and T-7, the expanded T-2 (m. 7) the basic ICC at T-2 and T-
9, and the expanded T-7 (m. 8) the basic ICC at T-7 and T-2, with only a -few PCs differing in each case.
Moreover, there are similarities in PC and element content
between the expanded ICC, the basic ICC, the PC collection in m.
13, and the ICC of "II" (Ex. 2-6).
Example 2-6. Expanded ICC at T-0 and its relationship to other PC collections in "I" and "II".
ICC OF T AT T-0:
7 EXPANDED ICC AT T-0:
9 \}0\o
•I", T-0 (H. 131 / MP, T-10
ICC OF *ir AT T-I:
UnilUe the harmonies of mm. 1-5 and 10-13, where all PCs of
a given T-level are verticalized or vertically oriented in a
single harmonic unit, the expanded PCCs of mm. 6-8 are partially
subdivided into subset collections or, more specifically, subset
harmonies. The subdivided PCs form more than one harmonic unit,
each with its PCs vertically oriented. Individual subset harmo•
nies have PCs that differ with those of other subset harmonies
and other PCs that are invariant; hence, the designation "par•
tially subdivided." This represents a step towards the complete
linearization or linear presentation of a T-level's PCs, in the 30 sense that a T-level's PCs can be subdivided into more and more subset collections to the point where the subsets are actually individual PCs. Such linearization characterizes later works by
Roslavets, although the initial T-levels o-f mm. 6 and 7 (T-ll) in "I" are linearized, as is T-ll (m. 7) o-f "III". (The tertian harmonies, implied by the successions o-f pitches in these lin• earized T-levels, are examined in Chapter Three.) Such T-level subdivision, as well as differences in chord structure and tex• ture, distinguish mm. 6-8 as a formal unit. Similarly, there are subdivisions of T-levels into subset collections in mm. 6-8 of "II" (T-2, T-10, and T-8), and m. 4 of "III" (T-7, T-O, and
T-5). Thus all such T-level subdivision occurs in middle, de• velopmental sections of the pieces. In contrast with "I" and
"II", there is a greater tendency towards these harmonic subsets and linearizations in "III", with the texture being less homo- phonic and more contrapuntal. These distinctive features of
"III" are examined later in this chapter.
ICC of "II"
As in "I", one ICC is the basis of all harmonic and melodic structures in "II".1"* Example 2-7a shows the referential PCC which realizes the ICC of "II", and Ex. 2-7b, based on Gojowy's analysis,20 shows the piece's PCs segmented into T-levels. 31
Example 2-7. The ICC of "II", and PCs partitioned into harmonies.
(a)ICC of "II":
o o
ELEMENT: 0 1 3 4 6 8 9 11 0
MEASURE: ID 121 (31 PITCHES 2 5t hi v—i *p- i . W J u. 4 3 2=2: -r SCALAR PRESENTATION OF PCCS T-LEVEL: O 3 8 1 I 10 I _L ZZZE 133 141 \± hi 5£ i^j 1*. X» 1 * -9—r s w —w 3 10 3 a—TT^* rtT L hf^r i__Jr<,Jy«__.. yjarr*^ A'?- 7T 32 33 Gojowy shows no variant element in his -form o-f the ICC, but Perle includes a variant element "1" (i.e., not part o-f the re• ferential PCC), bracketed in Ex. 2-7a. Element "1" only occurs in mm. 6-8 in the bass-line in partial arpegg i at i ons o-f the T-2 (m. 6), T-10 (m. 7), and T-8 (m. 8) harmonies, respectively.21 The occurrence o-f T-levels with element "1" in mm. 6-8 o-f "II", in the middle development section o-f a recapitulative ternary •form, is similar to the use o-f expanded ICCs in mm. 6-8 o-f "I", and contributes to the -formal role o-f these measures. Unlike variant element "10" in "I", however, variant element "1" in "II" is not associated with less significant functions in the melodic-harmonic structures. It plays an important role in a conventional tonal interpretation of the harmonic structures, a topic to be treated more fully in Chapter Three.22 The ICCs of "I" and "II" are quite similar. Gojowy notes that the PCs of the ICCs of "I" and "II" are inversional1y re• lated.23 In fact, the T-levels of "II" could be redesignated as T-levels of the PCC of "I" itself, with the initial PCC of "II" as T-ll of the PCC of "I". However, the above-mentioned variant elements in the PCCs of "I" and "II" make it difficult to ex• plain PC organization in "I" and "II" in terms of a single ICC. 34 ICC of "III" Unlike "I" and "II", which have a limited number of vari• ations o-f their respective ICCs, "III" apparently has seven variations o-f its ICC i-f we -follow the segmentation of pitches suggested by Gojowy's presentation of T-level successions.2"* Example 2-8a presents these variations at T-0, each labelled with a lower case letter. To the right of these PC collections is a list of T-levels of these variations, with the indications of measures in which they appear. Those variations with letters "a" to "d" correspond to Gojowy's four ICCs for the piece. In• cluded with these is Perle's "set" with bracketed variant ele• ments "9", "10", and "11". Example 2-8b illustrates the segmen• tation of pitches into PC collections, similar to the analyses of Exx. 2-3b and 2-7b. 35 Example 2-8. The ICCs o-f "III". (a)Seven variant ICCs, with T-levels and locations; Gojowy's -four ICCs (a, b, c, d) and Perle's single ICC with variant elements: ELEMENTS: 01234 6 89 10 11 60J0VY a a: T-O.T-5 (N. 1) T-S (N. 12) b: T-l.T-4 (N. 3) W.T-0 (N. 4) c: T-8.T-3.T-7, T-10 (N. 2) T-ll (N. 7) T-2 (NN. 8, 10- lD I T-5.T-0, T-4.T-7 (N. 13) T-0 (NN. 14-15) i: T-8 (NN. 3-6) T-6 (H. 8); T-9 (N. 9) e: T-l IN. 3) f. T-5 «N. 4) mJOLm L,, 9: T-0 (N. 12) L . L . Iv li PERLE ff= 36 Example 2-8 continued. (b)"111" segmented into PC collections: MEASURE: [11 (21 PITCHES 3 I 1 5? 3E SCALAR PRESENTATION OF PCCs T-LEVEL: 0 S I 8 JUL. (2) (31 [41 HP J i 33 s I I i 10 I 1 4" - ' 7 J 37 38 The differences between the ICCs cited by Gojowy and Perle reflect the i nc 1 us i veness o-f their respective ICCs. While Gojowy uses -four ICCs (with no variant PCs) to account -for the most -frequently occurring collections or their transpositions, Perle has only one ICC with three variant PCs. Although Gojowy's ICCs and T-levels account -for the PC con• tent o-f most harmonies in "III", the concept o-f -four different ICCs employed in "III" is problematic. Why should the final piece of this set be deemed so radically different from "I" and "II" in terms of compositional technique that it should embrace four ICCs, especially in light of its smaller dimensions? More• over, the perception of four distinct harmonies based on these four different ICCs would be unlikely. Perhaps the strongest indicator for the use of one ICC is the rather unique musical orthography of the ICC of "III" (i.e., the mixture of sharps and flats as accidentals in the scalar presentation of the ICC PCs, and PC intervals formed), and the consistency with which pitches of individual collections in the music conform to interval lie relationships suggested by the ICC PCs (Fig. 2-1).20 39 Example 2-9. Musical orthography of the ICC o-f "III" (a)ICC at T-0: T-0 LEVEL PCs: 6 - 61 - Bb - B - Db - DI - ELEMENT: 0 1 3 4 6 8 9 10 11 0 PC INTERVALS 12 12 2 1 1 11 i CNRONATIC SENITONE (AUGMENTED PRIME) DIATONIC SENITONES (NINOR 2NDS) DOUBLY AU6NENTED PRIME DIMINISHED 3RD CHROMATIC SENITONE DIMINISHED 3RD CHROMATIC SEMITONE (b)T-levels in "III": MEASURE: 111 [2] T-LEVEL: O C2) 131 7 10 1 (3) (3) 141 4 7 (3) (3) (3) 40 Example 2-9 continued. (41 (5-6) [71 [8) 5 8 11 2 ii) $~—^—LT n y-n+v0 'v>^" ——- (81 [?] [10-111 [121 6 9 2 5 t rial As'*'*** , , Ljljii *v*— [121 [131 0 5 04 0) (131 (14-151 7 0 Note: Boxed pitches are those elements (e.g., "9", "10", "11") not occurring with every T-level, and bracketed in Perle's "set". Elements missing from a T-level are indicated by a gap in the scale and a bracketed element number above the staff. Pitches that are added to the T-level are included in the scale with brackets. Finally, pitches that are enharmonical1y named in the music, as to the ICC at T-O, are included in the scale with the name (based oh the ICC) above or below as a bracketed solid notehead. Thus the musical orthography strongly suggests that a single ICC is the source for the PC collections of "III". (Hence, Gojowy's observations to the contrary are discussed in Appendix B.) Some variations shown in Ex. 2-8a cannot be ade• quately explained as forms of any of the suggested ICCs. For example, the initial collection of m. 3 (T-l) includes elements "11" (G) and "3" (B)j Gojowy designates this PCC as "irregular." 41 These additional elements can be thought o-f as belonging to the second T-1 harmony in m. 3 (Ex. 2-10). Example 2-10. PC collections, m. 3. T-1 T-1 T-4 This second T-1 collection o-f m. 3 is tranposed at T-4 (m. 3), and T-7 and T-O (m. 4). Perle in -fact cites these PC col• lections as evidence that Roslavets consistently omits specific elements (in this case, elements "3" and "11") to produce vari• ant T-levels.** Similar to the omitted B (element "3") of the second T-1 harmony, m. 3, and its occurrence in the preceding (T-1) harmony, element "3" PCs, omitted from T-4 (D, m. 3), T-7 (F, m. 4), and T-O (Bb, m. 4), are found in preceding harmonies (Ex. 2-11) 42 Example 2-11. Element "3" in mm. 3-4. As indicated earlier, the texture o-f m. 4 is strongly remi• niscent o-f mm. 6-8 in "I" where the three T-levels (T-O, T-2, and T-7), embodying a multiple transposition o-f a melodic-har• monic -figure, are each subdivided into three separate "subset" harmonies. Finally, Ex. 2-12 demonstrates that the second PC collec• tion o-f ro. 12 (T-O) is a modified inversion of that of T-0. 43 Example 2-12. T-0 collection, m. 12, as an inversion of ICC at T-O. PCs: Db - Eb - 6b - 6 - Bbb - Bb - B - Db INTERVAL*. 2 3 12 112 ICC AT T-0 PCs: Ob - 01 - E - F - 6 - 61 - Bb - B - Db INTERVAL: 2 112 1 2 12 Ultimately, the ICC indicated by Perle proves to be most useful as the unbracketed elements occur in at least 80% of the T-levels o-f "III", and the bracketed elements less often. Ele• ment "2" occurs only once and is logically not included in the PCC, although element "11" might as well have been excluded too as it occurs only twice in the entire piece. Two-thirds of occurrences of these variant elements in "III" are decorative or otherwise structurally less significant pitches (i.e., occurring as inner-voice pitches, and/or having short durations). Hence, there is a relationship, although not altogether consistent, between element occurrence and the func• tion or relative structural importance of the variant element. With the ICCs established, the groundwork has been laid for the subsequent discussion of harmonic successions and the asso• ciated T-levels.23* 44 Harmonic Successions and Successions of Transposition-Levels The study of harmonic successions in Trois Compos it i ons in• volves, to a large extent, the study o-f successions o-f T-levels. As has been explained, the PC content o-f a single harmony in a given piece is, with some exceptions, ultimately based on the PC content o-f one T-level o-f the ICC associated with that piece. This study will initially be concerned with transpositional re• lationships o-f adjacent T-levels in a harmonic succession, and transpositional cycles which -form the basis o-f many such adja• cencies in Trois Compositions. This section and the one suc• ceeding it will tentatively establish which T-levels are harmon• ically significant in the pieces. Transpositional Relationships o-f Adjacent T-Levels One o-f the characteristics o-f harmonic successions in Trois Compositions involves the transpositional relationships o-f adja• cent T-levels and the -frequencies o-f occurrence o-f such rela• tionships (Fig. 2-1). 45 Figure 2-1 Transpositional relationships between successive T-levels in "I", "II", and "III". (a)T-levels and IC relationships: •r MEASURE: I 5 6 8 10 T-LEVEL: 0-3- 10 1-4 7- 10 -4 11 -9-2 5 11 -0 11 -2 7 3-6 PC INTERVALS: 37 3333 6 7 10 5 3 6 1 11 3 5 8 3 IC: 35 3333 652536113543 10 11 12 13 6-3-6-9-4-9 0 9 3 7 5 3 3 3 5 5 3 •IV MEASURE: 12345678 9 T-LEVEL: 0-5 8-1 10 -3 10 -3 6-9 2-5 10 -3 8- 11 -4 7 PC INTERVALS: 535957533535553 53 IC: 535355533535553 53 9 10 11 12 13-14 7 0 - 5 0 - 5 0 0 5 5 7 5 7 0 5 5 5 5 5 0 •ur MEASURE: 1 2 3 4 5,6 7 8 9 10,11 T-LEVEL: 0-5 8-3-7- 10 1-1-4 7-0-5 8 11 2-6 9 2 PC INTERVALS: 53743 30335533 3435 IC: 53543 30335533 3435 10,11 12 13 14,15 2 -5-0 5-0-4-7 0 3 7 5 7 4 3 5 3 5 5 3 4 3 5 46 Figure 2-1 continued. (b)Frequencies of occurrence of PC interval and IC relationships between adjacent T-levels in "I", "II", and "III": PC INTERVAL: llllO 3948576 •I": 1 1 1 11 1 13 3 2 •ir: 6 1 li 2 •IIP: 11 3 6 3 TOTAL: I l l 28 2 3 1 20 8 2 IC: l 2 3 4 5 6 •P: 2 l 12 1 6 2 •IP: 7 13 •HP: 11 3 9 TOTAL: 2 l 30 4 28 2 The IC relationships o-f adjacent T-levels occurring most -frequently are ICs 3 and 5, which Gojowy identifies as charac• teristic o-f many harmonic successions in Roslavets's works. In the succession o-f transpositional levels, definite regularities can be observed. The chromatic progression is definitely avoided, but, on the other hand, progressions by minor thirds are frequent, as are those by fourths and fifths.20 Transpositional Cycles of T-Levels Not only are adjacent T-levels usually related by IC 3 or 5, but there often appears a succession of several T-levels in which adjacent T-levels are related exclusively by one of these ICs, frequently ascending. For example, in "I", mm. 1-3 (see Fig. 2-la), the T-level succession T-IO,T-1,T-4,T-7,T-10 exclu• sively involves an ascending IC 3. Where T-x is followed by T-x+3, T-x+6, T-x+9, T-x+O, and so on (e.g., T-10, T-1, T-4, T-7, T-10), such a succession will be termed a T-level cycle, 47 specifically a PC-interval 3 cycle (or interval 3 cycle). There are in fact three interval 3 cycles: T-O, T-3, T-6, and T-9 (cycle 3-0)5 T-l, T-4, T-7, and T-10 (cycle 3-1)5 and T-2, T-5, T-8, and T-ll (cycle 3-2). The interval 5 cycle involves: T-O, T-5, T-10, T-3, T-8, T-l, T-6, T-il, T-4, T-9, T-2, and T-7. Such cycles of T-levels are the basis of harmonic succes• sions in the pieces.2" Oftentimes, however, only a few T-levels o-f a cycle are used be-fore a transference to another cycle or components thereof. In some instances, a single T-level of one cycle is interpolated with T-levels of another cycle. Moreover, a T-level of a cycle (especially an interval 3 cycle) may occur out of order with respect to other members of the cycle. "I". Figure 2-2a presents the T-level successions- of "I", illustrating the T-level components belonging to each interval 3 cycle, while Fig. 2-2b illustrates the relationship of these cycles to the interval 5 cycle. 48 Figure 2-2. T-level successions of "I" and IC cycles. (a)Interval 3 cycles and T-levels belonging to each, with underlying balanced pattern o-f succession: MEASURE 1 2 3 4 5 6 7 8 10,11 12 13 T-LEVEL CYCLES 3-0: 0--3 9 3--6--3-6--9...9--0 3-1: 10--1-4-7--10--4 7 4 3-2: 11...2—5——2 3-o: «« HHimillH...fW 3-1: IHIIHIIIIHIHII * t 3-2: H...IIHIHI...HW 3-0 .3-0 3-1. .3-1 3-2. (b)Ascending interval 5 cycle o-f T-levels, with T-levels "I" derived -from this cycle and the interval 3 cycles (indicated in brackets on the le-ft): INTERVAL 5 CYCLE*. 0-5-10-3-8-1-6-11-4-9-2-7-0-5-10-3-8-1-6-11-4-9-2-7-0 MEASURE: 1 T-LEVEL: 0- (3-0) MEASURE: I..! 2 T-LEVEL: IO 1 4- -10 (3-1) MEASURE: 3 T-LEVEL: 4 (3-D : • MEASURE: 4..: 5 6 T-LEVEL: 11-- -2— -5- -11- (3-2) MEASURE: 7 8 T-LEVEL: -11— -2-7 (INTERVAL 5) MEASURE: tn 10-11 12 T-LEVEL:(0-31...3 6 9 (3-0) : NEASURE: 12.: 13 T-LEVEL: 4- -0 49 Note: The T-level succession o-f "I" is indicated by following the horizontal dash line from left to right and continuing on the following line. In Fig. 2-2a, T-level successions are shown with components of the interval 3 cycles on separate lines. The transference from one interval 3 cycle to another is apparently based on a "balanced" (rather than a purely symmetrical) pattern of cycle appearance. The progression from cycle 3-0 (m. 1) to 3-1 (mm. 1-3) to 3-2 (mm. 4-7) and finally back to 3-0 (mm. 10-13) is not fully balanced unless one interprets T-7 (m. 8) and T-4 (m. 12) as references to the 3-1 cycle, of which these two T-levels are components. This 3-1 cycle occurs before the final 3-0 cycle (mm. 10-13). Such a progression of interval 3 T-level cycles is then the underlying balanced structure upon which the harmonic organization of "I" is based in part. The 3-0 cycle (with com• ponents in mm. 1 and 10-13) acts as the framework for the T- level successions of the piece, with the initial T-0,T-3 succes• sion (m. 1) being completed in mm. 10-13 (the recapitulation) with T-3,T-6,T-9,T-O. The two other interval 3 cycles, 3-1 and 3-2, involve most of the other T-levels, and are in some degree associated with the piece's development. The central 3-2 cycle (mm. 4-7) coincides with the approximate midpoint of "I". The three interval 3 cycles are components of the interval 5 cycle whereby each interval 3 cycle T-level (e.g., T-O, T-3, T-6, and T-9 of the 3-0 cycle) appears at a regular interval in the interval 5 cycle; in other words, every third component (see the top of Fig. 2-2b). One can thus relate the interval 3 cycles, whose components are isolated on separate lines in Fig. 50 2-2b, to the all-inclusive interval 5 cycle. The interval 5 cycle apparently controls the sequence o-f T-levels or, more spe• cifically, the transference from one interval 3 cycle to anoth• er. The interval 5 cycle, in conjunction with the interval 3 cycles, is also the basis for some incompatible interpolations (e.g., T-9, m. 4, and T-4, m. 12, among others). The initial T-0,T-3 (cycle 3-0, m. 1) transfers to the 3-1 cycle (mm. 1-3) by moving one T-level back on the interval 5 cycle (T-3 to T-10, m. 1). (Note the vertical dotted line in Fig. 2-2b connecting the T-level ending one horizontal line to that beginning another horizontal line. For ease of viewing, additional vertical dotted lines beginning at the top of Fig. 2-2b connect the interval 5 cycle to the aforementioned interpo• lated T-levels.) Once the 3-1 cycle is completed with T-4 (m. 3), there is a transference to the 3-2 cycle (mm. 4-7), also by moving back one T-level on the interval 5 cycle. Similarly, the interpolating T-4 level in m. 12 (i.e., component of the 3-1 cycle interpolated in the 3-0 cycle of mm. 10-13) is derived from the interval 5 cycle through a reversal in direction in the cycle's order. Another interpolated T-level, T-9 in m. 4 (i.e., component of the 3-0 cycle interpolated in the 3-2 cycle of mm. 4-7), is likewise explained by a similar procedure. In other words, such transferences and interpolations involve interval 7 relationships between the T-levels in question. The other sig• nificant T-level succession not explained by interval 3 cycles, the T-0,T-2,T-7 sequence (mm. 6-8), is based in part on a rota• tion of the T-2,T-7,T-O portion of the interval 5 cycle. 51 In conclusion, the interval 5 cycle--in conjunction with the interval 3 eyeles--would appear to be the basis of most successions in "I", especially the aspects o-f transference and i nterpolati on. "II". The T-level successions o-f "II" are based on the in• terval 5 cycle. Figure 2-3 shows the cycle is modified, how• ever, because certain T-levels are omitted, and inserted else• where in the piece. These transferred T-level successions are labelled as A, B, C, and D in Fig. 2-3. Figure 2-3. T-level successions of "II" and the interval 5 eyele. MEASURE: 1 2 3-4 5 6 7 8 9 10-13 T-LEVEL: 0--5 8-1--10--3--6 -9.-2-5-10-3--8-11--4-7--0-5-0 Ca • a • Ba ••••aaaa Da a a a Aa a a a INTERVAL A... C... 0.... 5 0--5--10--3--8--1 -6--11--4--9-2 -7-0 CYCLE: B T-level succession C (T-10,T-3) and D (T-li,T-4) involve interval 5 cycle components out of sequence.30 Successions B (T-5,T-10,T-3,T-8, mm. 6-8) and A (T-O,T-5, mm. 10-12) are reca• pitulations of earlier successions; A recapitulates the initial succession of "II" following the completion of the interval 5 cycle. B would also seem to have some formal significance as it occurs in the development, beginning with the harmony associated with the melodic climax point of the piece. 52 "III". Figure 2-4 presents the T-level successions of "III" and the T-level cycles that are components thereof. Figure 2-4. T-level successions o-f "III" and the T-level eye 1es. (a)Surface successions: MEASURE: 1 3 4 5-6 7 8 9 10-11 12 13 T-LEVEL: 0--5--8—3--7--10—I~4—7—o~5—8—11—2-16-9)-2 5- io) -5 CYCLES: 1 I ( ) ( ).T 3-1 * * 3-2 INTERVAL 5 MEASURE: 8 9 10-11 T-LEVEL: 2—6—9—2 1 1 1 1 1 MEASURE: 12 13 : : : 14-15 T-LEVEL: 5--0--5-0-4--7-0 (b) Under 1 y i ng symmetrical T-level structure o-f "III": MEASURE: 1 2 3 4 5,6 7 8 9 10 12 13 14 T-LEVEL: 0-5 8-3-7-10 1-4 7-0-5 8 11 2-6 9 2 5-0 5-0-4-7 0 0(5) 7 7-0-5 5 (7)0 3-1 INTERVAL 5 3-2 The T-level successions o-f mm. 2, S-iO, and 13-15 (shown on the left side of Fig. 2-4a) are related in part through transpo• sition as the dotted vertical lines suggest. Harmonic-melodic figurations in mm. 1-2 are transposed with modifications in mm. 12-13, while the final two phrases (mm. 8-11 and 12-15) cadence on transpositions of the same arpeggiated figuration. The other T-level successions involve cycles 3-1 (mm. 2-4) and 3-2 (mm. 4- 13), connected in m. 4 by an interval 5 cycle segment (T-7,T-O, T-5). The complete 3-0 cycle does not occur in adjacent T- levels as do the other IC-3 cycles. In a sense, cycles initiated by T-7 in mm. 2-4 and T-5 in 53 mm. 4-13 involve prolongations o-f these T-levels. In this con• text, prolongation refers to a situation whereby a T-level is reiterated, with a limited number of other T-levels between the initial occurrence and the reiteration. Invariance of the reit• erated T-level's PCs through the intervening T-1eve 1(s)--espe• cially in the form of pitch continuity—facilitates the percep• tion of T-level prolongation. Particularly when the intervening T-levels are related to the reiterated T-level and to each other by ICs 3 or 5, there is a greater incidence of PC invariance. Such PC invariance in IC-3-related T-levels or, more specifical• ly, in T-levels of an interval 3 cycle, will be examined in a later section of this chapter; a discussion of prolongation is to be found in Appendix B. Hence, there is a simpler symmetrical structure involving T-O, T-5, and T-7 underlying the T-level successions (Fig. 2-4b). T-5 and T-7 are symmetrically related to T-O (i.e., interval 5 above and below). Because of this symmetrical structure, m. 4 is an apparent focal point of the piece. Surface features such as the octave ascent in the melody and inner voices contribute to this mea• sure's significance. Similarly, mm. 6-8 in "I" appear to be a focal point of that piece, aside from melodic, harmonic, rhyth• mic, textural, and formal reasons. The harmonic successions of "I", like those of "III", are generally based on interval 3 T- level cycles with the exception of mm. 6-8, where the interval 5 cycle segment (i.e., T-O,T-2,T-7) occurs. The fact that T-O follows, rather than precedes, T-2,T-7 in the interval 5 cycle does not diminish the significance of the cycle's appearance. 54 Moreover, both mm. 6-8 in "I" and m. 4 in "III" involve the sub• division o-f T-level PCs o-f three successive T-levels each into three distinct, subset harmonies, with the multiple transposi• tion o-f the initial three-harmony -figuration in each case. This similarity also rein-forces the overall similarities of these measures and their -function in the respective pieces. Based on this preliminary study o-f harmonic and T-level successions, one can say that "II" and especially "III" involve a tighter control o-f harmonic organization than "I" because o-f this greater reliance on interval 3 and 5 cycles as bases -for successions. This limitation o-f harmonic successions to certain -formulae is a distinctive characteristic o-f Roslavets's composi• tional technique.31 T-Level Occurrences and Their Rhythmic Characteristics: Towards a Hierarchy o-f T-levels The analytical examples indicate that certain T-levels oc• cur more frequently than others. This suggests that certain T- levels are more significant in the harmonic structure of the pieces, so that there is in fact a hierarchy of T-levels. Such a hierarchy might be based not only on T-level frequency of oc• currence but also on the total time-spans alloted to individual T-levels throughout each piece, and on the location of T-levels in relationship to formally significant time-points. This hier• archy itself suggests a form of tonality since tonality involves in part "the hierarchic ordering of PC factors" whereby "pitch content is perceived as functionally related to a specific 55 pitch-class or p i'tch-c 1 ass-comp lex of resolution."32 These dif• ferent aspects of T-level occurrence, which essentially concern T-level rhythmic characteristics, are examined in this section to infer such a hierarchy of T-levels. To begin, the harmonic rhythm of T-levels in the three pieces is individually analyzed. Harmonic rhythm of "Z". Example 2-13a presents the harmon• ic rhythms of T-levels in "I" with the time-spans of each T- level indicated by durational notation independent of pitch. A chart indicating the form of "I" is also included (Ex. 2-13b), for the purpose of analyzing T-level location in relation to formally important time-points. Example 2-13. Harmonic rhythm and form of "I". (a)Harmonic rhythm of "I": MEASURE: 1 2 3 4 5 6 7 T-LEVEL: 0 3 10 1 4 7 10 4 11 9 2 5 11 0 11 2 DURATION OF T-LEVEL: li •>) V\- J J iU RHYTHM OF SUBSET HARMONY: MEASURE: 8 9 10 11 12 13 T-LEVEL: 7 36369490 (J- c) 3J< J J 0 J J J. P 56 (b)Form of "I" (modified recapitulative ternary form) : C A3: expos i t i on mm. 1-3 1st phrase m. 1 tc3 m. 2 Cc3 mm. 1 and 2 (Cc3-extension) have 4 modifications of initial motive, m. 1 m. 3 Cd3..... cadence (with elision, into m. 4) mm. 4-5 2nd phrase m. 4 [c*1....initial figuration transposition of initial figuration, m. 1, followed by repetition of another modifica• tion (arpeggiations) of initial mot i ve m. 5 Ce3 ..... cadence (with elision, into m. 6); 3-2 T-level cycle components in mm. 4-7 might suggest mm. 4-5 as beginning of development CB3: development/new material mm. 6-9 3rd phrase m. 6 Cf-g3 m. 7 Cf*-g'3.initial figuration, m. 6, repeated with modifications in m. 7 m. 8 Cg"3....modified transposition of Cg3, m. 6 in mm. 7 and 8; abrupt cadence, m. 9 with rest CA'3: modified recapitulation mm. 10-13 4th phrase m. 10 Cc"3 m. 11 Cc"3...mm. 10-11 modified (arpeggiated) transposition of m. 2 figurations m. 12 Cc" 3 . .modif led Cc"3 m. 13 Cc""3..cadence; mm. 10-13 have limited similarities with mm. 1-3 In mm. 3-4 and 8-9 (Ex. 2-13a), there are bracketed rhythms above the staff that indicate the time-spans of harmonies (i.e., T-4 and T-7, respectively) including rests which follow. Par• tially because of the irregularity produced in the harmonic rhythm by such rests and the sense of deceleration, the T-4 and T-7 harmonies (mm. 3-4 and 8-9 respectively) delineate phrases. 57 The harmonic rhythms o-f T-level successions in "I" play an important role in delineating form. For one thing, variances in the time-spans o-f harmonies concur with apparent -formal divi• sions. In mm. 1-5 (the initial "A" section of the ternary form), the most common and shortest time-span of the individual harmonies is the quarter value, with longer half- and dotted- half values found at phrase beginnings and in m. 5, the final measure of this section. Measures 10-13 are similar, with quar• ter-value harmonic rhythm and the dotted-half-value in m. 13. In contrast, the harmonic rhythm of mm. 6-9 is more complex. If one defines the harmony in terms of the T-levels (both basic and expanded), the most common and shortest T-level time-span of mm. 6-9 is the dotted-eighth value. This indicates a deceleration in the harmonic rhythm between mm. 1-5 and mm. 6-9, and a conse• quent acceleration (mm. 6-9 to mm. 10-13). On the other hand, if the rhythm of the subset harmonies is taken into considera• tion, then the most common and shortest T-level time-span of mm. 6-9 is the eighth-value, which indicates an acceleration and consequent deceleration involving mm. 1-5, 6-9, and 10-13, res• pectively. However one perceives harmonic rhythm in mm. 6-9, the acceleration and/or deceleration concurs with changes in other musical parameters (e.g., the compound rhythm, and meter) in these measures. Har-monic r-hythm in "II". Example 2-14 presents the harmon• ic rhythm and form of "II". 58 Example 2-14. Harmonic rhythm and -form o-f "II MEASURE: 1 2 3,4 5 6 7 8 T-LEVEL: O 5 8 I 10 3 6 9 2 5 10 3 8 11 4 DURATION OF T-LEVEL: X4. MEASURE: 9 10 11 12 13 14 T-LEVEL: 70 5 0 5 0 0 3J< *) J J J JJ (b)Form o-f "II" (recapitulative ternary -form): CAD: exposition mm. 1-5 1st phrase mm. 1-2 Cc3 mm. 3-5 Cc'3..two-pitch motive with arpeggiated harmony repeated in mm. 1-45 2nd sub-phrase unit Cc'3 has repeated T-level succession (T-10,T-3, mm. 3-4), extended by repetition o-f m. 4, melodic figure in m. 5; continu• ation into CB3 without cadence (un• less in m. 6, T-2,T-5) CB3 development/new material mm. 6-9 2nd phrase m. 6 Cd3 m. 7 Cd'3 mm. 8-9 C d " 3 .. cadence- 1 i ke -figuration with simul• taneities repeated in transposition in mm. 6-85 extension with cadence in mm. 8-9 59 Example 2-14b continued. CA'3 recapitulation mm. 10-14 3rd phrase mm. 10-12 Cc3.m. 1 progression repeated m. 13 Cd"' 3 ... transposed simultaneity -from CB3 •for -final cadence chord What differentiates "II" from "I" and "III", among other things, is the regularity of harmonic change through much of the piece, namely the common quarter-value time-span of most harmo• nies. The only irregularities occur in mm. 9 and 11-14 (Ex. 2- 14) because of rests following the harmonies, again interpreted as silences through which harmonic perceptions continue. In these measures, rhythmic deceleration, a factor in cadence, results. Unlike the difference in the harmonic rhythm of mm. 6-9 in "I" (i.e., another indicator of the ternary form), the harmonic rhythm of "II" is generally regular and thus not a factor in the perception of the formal distinction of mm. 6-9. Harmonic rhythm of "III". Example 2-15 presents the harmonic rhythm and form of "III". 60 Example 2-15. Harmonic rhythm and form of "III". (a)Harmonic rhythm, with time-spans of harmonies given below: MEASURE.' 1 2 3 4 5 6 7 T-LEVEL: O S837101 4703 8 11 DURATION OF T-LEVELS! j j J ; 1 « ~ ------^j;^ TIM-SMNS:U> 564242 10 2435 19 17 MEASURE: 8 9 10 11 12 13 14 IS T-LEVEL: 2 6 9 2 5 0 5 0 4 7 6 J. 77 J. J* 5J. c/ JNJ- W 6 6 19 5 6 4 2 4 2 13 12 CA3: exposition mm. 1-2 1st phrase m. 1 C c 3 m. 2 Cd3 continuation into m. 3, with no cadence mm. 3-6 2nd phrase (continua- m. 3 Ce3 initial figuration has limited tion of similarities with initial fig- exposition uration, m. 1 with new m. 4 Cf3 climaxing action, consisting material) of two-fold modified transpo• sition of three-harmony fig- urat i on mm. 5-6 Cg3 ...... highpoint or cadence of cli• maxing action of m. 4 m. 7 Ch3 bridge to "B" 61 Example 2-15 continued. CB3: development/new material mm. 8-11 3rd phrase m. 8 C i 3 m. 9 C i ' 3 . modified repetition of 2nd figuration, m. 8 mm. 10-11 Cj3 .... cadence CA'3: modified recapitulation mm. 12-15 4th phrase m. 12 Cc'3 modified transposition of m. 1 m. 13 Cd'3 modified transposition of m. 2 mm. 14-15 [j']...transposition of mm. 10-11 The harmonic rhythm in "III" varies constantly, in contrast to the consistent harmonic rhythm of "I" and "II". Moreover, the initial time-points of some harmonies do not coincide with the notated barline, examples of such being T-O 4), T-ll (m. 7), T-5 (m. 12), and T-O (m. 14). Up to m. 5 there are relatively short harmonic durations, except for T-l tively sudden deceleration in the harmonic rhythm, after which there is some degree of acceleration with m. 8, and another pe• riod of deceleration with mm. 9-li. The recapitulation (mm. 12- 13) represents an acceleration, with shorter harmonic durations, followed by a final deceleration at the cadence (mm. 14-15). There are certain relationships between harmonic rhythm and form in "III". Some single T-levels of longer duration coincide with, or occur in close proximity to, cadences or formally im• portant time-points: T-8 (mm. 5-6)5 T-ll (m. 7), a melodic "bridge" to the resumption of harmonic activity in m. 85 T-2 62 (mm. 10-11), preceding the modified recapitulation of mm. 1-2 in mm. 12-13; and T-O (mm. 14-15), the final measures and exact transposition of T-2 harmony (mm. 10-11). The longer durations, and the sense of deceleration produced thereby, contribute to the effect of cadence. Interestingly, each of the four afore• mentioned time-spans is approximately nine eighth values in durat i on. Hierarchy of T-levels Figure 2-5 presents a hierarchy of T-levels in the individ• ual pieces and in Trois Compositions as a whole, based on fre• quency of occurrence and total time-spans. In Fig. 2-5c, the T- level hierarchies for the individual pieces (Fig. 2-5a and 2-5b) are combined by averaging.33 Figure 2-5. Hierarchy of T-levels based on frequency of occurrence and total time-spans. (a)Hierarchy of T-levels from most significant to least based on frequency of occurrence'. DESCENDING HIERARCHIC ORDER, LEFT TO RIGHT "I": 0 2/3/4/7/9/11 6/10 (1 / Si NO 8) •II": 0 5 3/10 8 (1/2/4/6/7/9/11) •Iir: 0 3 7 2 / 4 / 8 (1 / 3 / 6 / 9 / 10 / 11) T-'Iir: 0 5 3/7 2/4/ 10 9 / 11 6/8 1 63 Figure 2-5 continued. (b) Hierarchy o-f T-levels based on total time-spans: •I': 0 11 4/7 3/5/9 2 6/ 10 1 •II": 0 5 3/ 10 8 7 1/2/4/6/9/ 11 •III': 0 8 2 / 5 11 9 1 / 7 4 / 6 3 / 10 •r-'III": 05 11 287934 10 1/6 (c) Hierarchy o-f T-levels based on combination o-f (a) and (b), above: •I": 0 11 4/7 3/9 2 3 6/10 1 •11". 0 5 3/ 10 8 7 1/2/4/6/9/ 11 •Iir: 058274 11 9163 / 10 •I'-'Iir: 03723 / 11 48/9 10 16 Note: In (a), T-levels indicated in brackets are those that occur only once. The solidus separates two or more T-levels which are determined to have the same degree o-f significance, based on -frequency o-f occurrence and total time-span. T-O is most important in all three pieces, based on occur• rence and total time-span, and because it is the -first and -final T-level o-f the individual pieces. This strongly suggests that it functions as a referential sonority, or "tonic," in each piece. In "II" and "III", and overall in the pieces, T-5 is the second most important T-level, while in "I", T-ll is the most important T-level after T-O. While T-5 and T-ll frequently oc• cur with T-O in T-level successions in the respective pieces at formally significant time-points, it is difficult to make analo• gies with conventional tonality and its hierarchy of chords, es• pecially tonic and dominant chords. Perhaps the function of T-5 and T-ll with respect to T-O is best described as auxiliary, es- 64 pecially when the former occur between reiterations of T-0. Certain conventional tonal implications of these T-level hierar• chies are, however, explored in Chapter Three. T-levels that are significant due to their roles in specif• ic IC cycles are also significant in the hierarchies illustrated in Fig. 2-5. For example, in "I", T-ll (m. 4) is the initial 3-2 cycle T-level, and T-3 "III", T-0, T-5, and T-7 are important in the underlying symmet• rical structure which is centered at m. 4. T-level significance, besides being determined by frequency of occurrence and total time-span, is also suggested by occur• rence in relation to formally important time-points. On occa• sion, the reiteration of a particular T-level will coincide with another formally important time-point. Such T-level occurrences at formally important time-points are examined below in the in• dividual pieces. T-level Occurrences and Their Relationships to Form "I". In addition to reasons cited above, T-0 is more sig• nificant because of its occurrences in the first and final for• mal sections, which help to delineate the recapitulative ternary form of "I". Perle notes the relationship of T-level recurrence to form: "The larger formal implications of controlled transpo• sitional relations are realized to a limited extent in • the derivation of the concluding bars of the first piece from trans- 65 positions o-f the set that are closely related in PC content to the original statement o-f the set."3'* In addition, T-O occurs in m. 6, at the approximate midpoint o-f "I". T-ll initiates the second phrase (mm. 4-5) with an exact pitch transposition o-f the T-0 harmony (m. 1), and initiates the middle section (m. 6), and recurs within it (m. 7).3*31 Interest• ingly, the T-11,T-0,T-11 succession (mm. 6-7), employing the two most significant T-levels in "I", occurs in the middle -formal section, and strongly implies two conventional tonalities, which are discussed in more detail in Chapter Three. T-4, T-5, and T-7 are used to terminate the -first, second, and third phrases, respectively. T-3, which succeeds T-0 (m. 1), initiates the recapitulation and recurs in it, in m. 11. Other T-levels which recur in similar situations are T-2 (mm. 4 and 7), as part o-f cadential harmonic successions, and T-4 (mm. 2 and 12), decorating or connecting more important T-levels in cyclic progressions. Hence, T-O, T-ll, and, to a lesser extent, T-3, T-4, T-5, and T-7 can be considered to be the most signifi• cant T-levels in "I" both because of their positions within the T-level hierarchies (Fig. 2-5) and because of their locations in relation to the piece's form. "II". There are a few points of interest concerning the relationship of T-levels to form. First, the T-0,T-5 succession (mm. 1 and 10-12) is one indicator of the recapitulative ternary form. Interestingly, the only other occurrence of T-5 takes place in m. 6 (T-2,T-5), the first measure of the middle sec- 66 tion, with the T-2 sonority containing the highest melodic pitch o-f the piece. Another succession o-f interest is T-10,T-3 (mm. 3, 4, and 7), occurring in both the -first and middle -formal sec• tions, although neither T-level occurs elsewhere in "II". Sur• face -features o-f the three occurrences betray no similarity (other than the PC content o-f the harmonies), so that there is no readily perceivable connection between the two formal sec• tions due to this recurrence. Finally, the only occurrence of T-7 (m. 9) concludes the middle section (mm. 6-9), like that of "I" (T-7, m. 8), and precedes the recapitulation (mm. 10-13) and its T-O,T-5,T-O successions.3* "Ill". T-O and T-5, which appear together in a number of harmonic successions in "III", occur at formally important time- points: m. 1, the first succession; m. 4, a focal point in the first part of "III", preceding the harmonic "repose" of mm. 5-7; and mm. 12-13, the modified recapitulation of mm. 1-2. The co• incidence of these T-levels with such time-points is quite simi• lar to that in "II", where T-O,T-5 begins the piece and is used in the recapitulation. (Of course, there are the formal impli• cations of T-O's appearance as the first and final T-level of "III", which Perle has noted.)35" Associated with recurrences of the T-O,T-5 T-level succes• sion are three other T-levels: T-4, T-7, and T-8. T-O,T-5,T-8 occurs in both mm. 1-2 and 4-6, the beginning and end of the first formal section. T-4,T-7,T-O occurs in mm. 3-4, in connec• tion with the approach to the harmonic repose of mm. 5-7, and 67 also occurs in mm. 13-15, the final cadence. T-4, T-7, and T-8 function as T-levels either following or preceding T-O and/or T-5, generally with adjacent T-levels related by ICs 3 or 5. One other T-level of significance is T-2, which initiates and concludes the first phrase of section "B" (mm. 8-11) of the ter• nary form of "III". In general, T-levels that are more significant, based on the hierarchies presented in Fig. 2-5, usually appear at formal• ly important time-points. Recurrent Harmonic Successions Components of the three interval 3 cycles and the interval 5 cycle of T-level successions recur, some with more frequency than others, and some in two or three pieces (Fig. 2-6). 68 Figure 2-6. Recurring T-level successions in Trots Compos ttions. (a)Frequent 1y (b)Multiple T-level successions: occurring T-level successions, with T-1 eve 1 IC Pi ece Measure the number of successions success i ons occurrences: T-O,T-5,T-8 5-3 "II" 1-2 T-O,T-5 "III 1-2 4-5 T-4,T-7 4 T-5,T-O 4 T-O,T-5,T-O 5-5-5-5 "II" 10-12 T-5,T-O,T-5 5-5-5 "III" 12- 13 T-2,T-5 3 T-3,T-6 3 T-4,T-7,T-O 3-5 "II" 8-10 T-5,T-8 3 "III" 3-4 T-6,T-9 3 13- 15 T-7,T-O 3 T-9,T-2 3 T-4,T-7,T-O,T-5 3-5-5 II " 8-10 T-10.T-3 3 III " 3-4 T-l,T-4 2 T-9, T-2, T-5 5-3 II J II 4-5 T-3,T-10 2 "II" 5-6 T-7,T-10 2 "III" 9-12 T-8,T-ll 2 T-10,T-1 2 T-6, T-9, T-2,T-5 3-5-3 "II" 5-6 T-ll,T-2 2 "III" 8-12 T-IO,T-l,T-4,T-7 3-3-3 II J II 1- 3 "III 2- 4 3-3 II J II 10-12 "II" 4-5 (c)Recurring T-level successions o+ two and more T-leveli M J II MEASURE: 1 2 3 4 3 6 7 8 10,11 12 13 T-LEVEL: 0—3—10 1-4 7-10-4 11-9-2 5 11-0 11-2 7 3-6 9-4-9 0 RECURRENT * * • * i ( )—• SUCCESSIONS: *—* MEASURE: 1 2 3,4 3 6 7 8 9 10,11 12 13 T-LEVEL: 0-5 8-1 10-3 6-9 2-5 10-3 8--11-4 7 0-5 0 0 RECURRENT * 1 t * * * SUCCESSIONS: t—• * * *—I I * * * 69 Figure 2-6c continued. "Ill ll MEASURE: 1 2 3 4 5,6 7 8 9 10 12 13 14 T-LE«EL: 0-5 8—3—7—10 1-4 7-0-5 8 11 2-6 9 2 5-0 5-0-4-7 0 RECURRENT J. J J J- * t f f- * SUCCESSIONS: i i f—f f { )—f Note: Recurring T-level successions are indicated above using "* with "*" denoting first and last sonorities of the re• curring successions. "#- ( ) indicates an interpolated T- level, not part of the recurring succession. In this figure, recurring two-T-level successions are only indicated when they are not part of multiple T-level successions. Based on Fig. 2-6a, only 44 of the 144 possible T-level successions involving different combinations of two T-levels are utilized in the three pieces (16 recurrent successions and 28 non-recurrent). Some of these frequently occurring two-T-level successions are components of multiple T-level successions (Fig. 2-6b), all of which have adjacent T-levels related by ICs 3 or 5. Figure 2-6c illustrates the recurrent T-level successions. Some successions, by virtue of their recurrences at formal• ly important time-points, have certain relationships to the forms of "I", "II", and "III". The succession T-0,T-5,T-8 be• gins "II" and "III" and occurs in mm. 4-6 of "III" at the con• junction of the interval 5 and the 3-2 cycles (mm. 4-7). Suc• cession T-7,T-O,T-5 occurs both in "II" (mm. 9-10) and "III" (m. 4), although the occurrences differ in function. Similarily, another cyclic succession, T-3,T-6,T-9, occurs in "I" (mm. 10- 12) and "II" (mm. 4-5), with each occurrence having a different formal function. As noted earlier, the cyclic succession 3-1 occurs in the first phrases of "I" (mm. 1-3) and "III" (mm. 2- 70 4). The succession T-9,Y-2,T-5 ("I", mm. 4-5) and its variant T-6,T-9,T-2,T-5 ("II", mm. 5-6, and "III", mm. 8-12) recur, co• inciding with important junctures: in "I", at the cadence of the -form's "A" section! in "II", linking the "A" section, mm. 1- 5, to the middle "B" section; and in "III", linking the -first phrase and cadence o-f the "B" section with the recapitulation in m. 12. Finally, there is the alternation o-f two T-levels in• volved in the succession T-O,T-5,T-0,T-5 which occurs in "II", mm. 10-14, and "III", mm. 12-13 (mm. 12-15, i-f interpolated lev• els are discounted), both o-f which are concluding successions. Those interpolated levels, T-4,T-7 with T-O -following, previous• ly occurred in mm. 3-4 o-f "III" and in "II", mm. 8-10 (i.e., T-4,T-7,T-O,T-5). To complete this study o-f the ICC system and the T-level successions underlying the harmonic progressions, the next sec• tions o-f this chapter will examine T-level successions as to PC content, and element occurrence and ordering, respectively. 71 Characteristics o-f T-Level Successions as to PC Content PC Invariance and Pitch Continuity With six or more PCs per T-level, there are a number o-f in• variant PCs in most T-level successions, and a number o-f these invariant PCs involve pitch continuity, that is, PC invariance in the same register. The number o-f invariants in a PCC and a transposition o-f it depends on the total IC content o-f the PCC, as indicated by the interval vector. Quite simply, with the in• terval vector o-f the ICC o-f "I" < not including element "10") be• ing C3 3 5 4 4 23, there are three invariants between T-levels related by IC 1, three between IC-2-related T-levels, -five be• tween IC-3-related T-levels, -four between IC-4-related T-levels, and -four between IC-5-related T-levels. In the case o-f IC-6- related T-levels, the interval vector number -for IC 6 (in this case, two) must be multiplied by two in order to determine the number o-f invariant PCs.3" Such invariance and continuity can affect one's perception of similarities and differences in har• monic progression. PC invariance and pitch continuity are examined in Exx. 2- 16 and 2-17. In Ex. 2-16, PCs of T-levels of the three pieces, in scale form, are compared on the basis of T-level IC relation• ships to illustrate differences in the numbers of invariant PCs. Boxes highlight these invariant PCs. Variant elements in each T-level are bracketed, with the implication that their absence in certain harmonic successions in the music will mean possibly fewer invariant PCs in those successions. •" 72 Example 2-16. Invariant PCs o-f IC-1- to IC-6-re 1 ated T-level< •r T-0 I T-0 L-I/L,,\ nan I t«i 1 II * nj 1 — —ILK- _ hn * 1« 1-1 l_m Jtf i /* * yo ELEMENT 9 10 0 1 8 10 NUMBERS: 0 1 4 T-4 T-l ELENENT NUMBERS: 0 3 8 9 8 9 4 6 T-0 T-0 J2ZE 0 3 6 8 10 0 13 6 8 9 T-2 T-5 bo ft? " 10 0 1 4 6 8 10 0 1 3 4 T-0 T-0 jzzz 0 1 3 4 6 9 0 3 4 6 9 10 T-3 T-6 A rr-\o ^0 9 10 0 1 3 6 6 9 10 0 3 4 73 Example 2-16 continued. •II' T-O T-O 0 1 4 0 1 3 4 T-l T-4 11 0 3 8 9 11 0 T-O T-O dh H <>0 P 0 1 3 6 8 11 01 4 6 8911 T-2 T-3 11 0 1 4 6 9 11 0 1 3 4 6 T-O T-O m -n & HP 0 3 4 6 9 11 0 3 6 9 T-3 T-6 ID 3sc |HH|°(n) T 9 0 1 3 6 8 6 9 0 3 74 Example 2-16 continued. •nr T-0 T-0 0 1 4 9 10 11 0 1 3 4 8 10 T-1 T-4 11 0 3 8 9 10 8 9 11 0 4 6 T-0 T-0 0 1 3 6 8 10 11 0 1 3 4 6 8 9 11 T-2 T-5 IT 10 11 0 1 4 6 8 9 8 10 11 0 1 3 4 6 T-0 T-0 •55 as 0 1 3 4 6 9 11 0 3 4 6 9 10 T-3 T-6 9 10 0 1 3 6 8 6 9 10 0 3 4 75 There may be as few as two and as many as seven PCs common to adjacent harmonies. IC-l-related T-levels in "I" and "II" (which occur very infrequently) usually have only four common PCs, while IC-3- and IC-5-related T-levels (which occur most frequently in all three pieces) have five to seven invariant PCs. Example 2-17 illustrates PC invariance and pitch continuity in the harmonic successions of the pieces. These harmonic suc• cessions are shown on the first of three systems, with pitch continuity highlighted in the second, and PC invariance (invol• ving different registers) isolated in the third, with lines con• necting the invariant PCs. A pair of numbers (the first un- bracketed, the second bracketed) for every succession indicates the total number of invariant PCs and pitch continuities, res• pect ively. Following the systems illustrating PC invariance and pitch continuity in a given piece, a graph—based on information pre• sented in the systems—visually illustrates the degree of chang• ing PC content in each succession, with the height of the solid line indicating the number of invariant PCs in each succession. An elevation in the line indicates less similarity because of fewer invariant PCs. In order to account for pitch continuity, an additional half-unit value is assigned to such pitches, based on one unit value per invariant PC as indicated on the left side of the graphs. Dash lines in the graphs illustrate pitch conti- nu i ty. 76 Example 2-17. PC invariance and pitch continuity in T-level successions p+ Trois Compositions. •r MEASURE: 111 121 131 T-LEVEL: O 3 io l 4 7 io PITCH COLLECTIONS: -to—^— HO JO F"rw— JN THW— %S—b PITCH CONTINUITY: b,-* Jit—- V PC INVARIANCE (WITHOUT PITCH CONTINUITY): 3(4) 4(1) 5(1) 5(11 5(2) 5(2) 2(1) 3(1) 4(2) 4(3) 4(2) 3(1) 4(2) 4(1) 78 Example 2-17 continued. [81 [10,111 (121 (131 «7 3 6 9 4 9 0 1^ tf/ =i- K» ^ M—^ ^8 | o Sf ^. remso=a»= l — j? isa i— • • t|0— — j \° 1 i>8 ! / !rt 1 ¥ —" \ Graph o-f changing PC content in "I": NUMBER OF INVARIANT PCs 0 1 2 3 4 5 , 1 1 1 'I 1 I ^rJU" I 6 j i 7 • T-: 0 3 10 1 4 7 10 4 11 9 2 3 11 0 11 2 7 3 6 9 4 9 0 N.: 1 2 3 4 3 6 7 8 10,11 12 13 79 80 Example 2-17 continued. (41 [SI (6) ' 3(01 5(4) S(l) 5(2) 5(2) 5(2) 3(2) 5(1) 4(2) 5(3) 4(2) 4(0) 4(0) 8(1) 81 Example 2-17 continued. Graph of changing PC content in "II": NUMBER OF INVARIANT PCs Li T-: 0381 10 3 10 36925 10 38 11 4705 0 0 N.: 12 3 456 78 9 10,11 12 13 "III" 5(0) 4(1) 3(2) 3(0) 3(0) 3(0) 7(1) 82 Example 2-17 continued. [31 [41 13,61 (71 [81 1 4 7 0 5 8 11 2 in J W i^H fci hi} fr* -43—- kg— ^ tg. fry i ftojft i*— 1 5HF- ^ —*a_hP A° 1 1 — w°te BO ha to '* y , t.n Jt.fl fro ^ i ^ -Jol ii— I :— <»— ... 0„_^O 1 2 =*e— 410) 413) 313) 3(3) 3(0) 3(0) 3(2) 191 [10,111 1121 [131 9 2 3 3 0 J2S- ^7* »? JFfr Iff tey t 3(2) 3(1) 4(3) 3(3) 4(1) 312) 3(2) 83 Example 2-17 continued. 3(0) 3(1) 3(2) Graph of changing PC content in "III" NUMBER OF INVARIANT PCs 0- 1- 2- 3- 4- 5- 6- -» • I-: 05837 10 147058 11 269 2 5050470 N.: 1 2 3 4. 5 7 8 9 10 12 13 14 In "I" and "II", IC-3-related T-levels generally have five invariant PCs, while IC-5-related T-levels have -four} in "III", there are on average four, and three invariant PCs, respective• ly- IC-1-, 2-, 4-, and 6-related T-levels which occur infre- 84 quently in all three pieces generally have fewer invariant PCs (i.e., usually between three and -four PCs) . When one compares the total number o-f successions in each piece and the total num• ber o-f invariant PCs, there are -fewer invariant PCs in "III" -for the number of harmonic successions, compared with "I" and "II". (There are in total slightly more invariant PCs in successions in "II" than in "I".) In other words, successions of "III" ex• hibit a greater degree of harmonic change, based on PC invari- ance. This is due in part to the frequent occurrence of PCCs with few or no variant elements. Moreover, PC invariance has certain, albeit limited, impli• cations for the forms of the pieces. In the first and final phrases of "I" (mm. 1-3 and 10-13, respectively), there is more PC invariance and pitch continuity than in mm. 6-8 (including progressions T-5,T-ll tmm. 5-6] and T-7,T-3 [mm. 8-10]). In mm. 1-4 and 9-13 of "II", there is less PC invariance and pitch con• tinuity than the middle section. In "III", mm. 1, 2 (from T- lO), 3, and 8-12 (the third phrase) have more PC invariance and pitch continuity than mm. 2, 4-8 (development), and 12-15 (reca- p i tu1 at i on) . An equally important factor in the perception of similarity in two harmonies is the extent of pitch continuity. Even with invariant PCs in a succession, it is difficult to perceive simi• larity in the two harmonies with little or no pitch continuity, as is the case with most harmonic successions in Trois Composi• tions. In going from "I" to "III", there is an increasing ten• dency for harmonic successions with no pitch continuity (i.e., 85 -from 11% to 33% of successions). Like PC invariance, pitch continuity has some implications for form. In "I", successions T-O,T-3 (m. 1), T-10,T-4 (m. 3), and T-9,T-O (mm. 12-13), with at least three pitch continuities each, occur at the beginning or at cadences. Successions T-4, T-ll (mm. 3-4) and T-5,T-ll (mm. 5-6), with no pitch continuity and fewer invariant PCs than preceding successions, span adja• cent formal sections. In "II", successions T-6,T-9 (m. 4) and T-4,T-7 (mm. 8-9), with at least three pitch continuities each, immediately precede new formal sections. In "III", successions T-4,T-7,T-O,T-5 (mm. 3-4, with the climaxing action of the first section, mm. 1-7) and T-9,T-2,T-5 (mm. 9-12, third phrase ca• dence and link to the recapitulation) have at least three pitch continuities in each component succession, although PC invari• ance is less in mm. 4-8. Structurally significant pitch conti• nuities include: C4 and Ftt/Gb4 ("I", m. 3), D4 ("I", mm. 12- 13), E2,3 ("II", mm. 8-9), and Attl ("III", mm. 7-8), all of which occur at cadences.3" PC Invariance in IC-3-Related T-Levels The greater number of invariant PCs in T-levels related by IC 3, the basis of interval 3 cycles which govern many T-level successions in the three pieces, supports the concept of T-level families based on T-levels comprising the interval 3 cycles (e.g., T-O, T-3, T-6, and T-9 of the 3-0 cycle comprising the 3-0 T-level family).-*0 In fact, there may be some basis for the notion of "modulation" from one T-level family (or component T- 86 level thereof) to another. In a given T-level family (in "I" and "II" at least), there is an invariant PC collection forming a conventional diminished-seventh chord (i.e., three superim• posed IC 3 intervals, elements "0", "3", "6", and "9" of each T-level), this collection being invariant to the four T-levels of the family. In "III", element "9" does not consistently oc• cur with every T-level; hence only three PCs of the invariant diminished-seventh PC collection of a family occur with any given T-level of the family. PC invariance in T-level families in all three pieces is illustrated in Ex. 2-18. In Ex. 2-18a, which presents T-levels T-0, T-3, T-6, and T-9 (T-level family 3-0) of "I", "II", and "III", four invariant PCs in each T-level of a family (i.e., the diminished-seventh chord) are highlighted with solid vertical lines, and indicated in Ex. 2-18b by open noteheads in a scalar presentation of T-level family invariant PCs. Those four PCs occurring in at least two of the four T-levels, referred to as "quasi-invariant PCs," are highlighted in Ex. 2-18b with solid noteheads. The other four PCs in a family occur with only one T-level, and possibly two, if variant elements are employed. The invariant and quasi-invariant PCs of T-level families 3-1 (T-1, T-4, T-7, and T-10) and 3-2 (T-2, T-5, T-8, and T-ll) in the three pieces are also illustrated in Ex. 2-18b. Interest• ingly, the PC collections shown in Ex. 2-18b are octatonic col- 1 ec t i ons. "*x 87 Example 2-18. PC invariance in IC-3-related T-level -families. (a)T-O, T-3, T-6, and T-9 in "I", "II", and "III": 'II' •III' T-O bo Wi^ 4 "1* ,-3 I bo loi 3iS T-6 £21 te T-9 315 (b) Co 1 1 ect i ons o-f invariant and quasi-invariant PCs o-f T-level -families 3-0, 3-1, and 3-2: T-LEVEL FAMILY 3-0: T-LEVEL FAMILY 3-1: T-l T-4 2Z zz T-7 E&,fr« T-10 T-LEVEL FAMILY 3-2: T-2 T-5 T-8 in T-U S3 Figure 2-7 presents the successions o-f T-level -families in the three pieces, based on the T-levels, and tables o-f T-level •family occurrences and total time-spans. Figure 2-7. Successions o-f T-level -families. M j M MEASURE: 1 2 3 4 5 6 7 8 T-LEVEL: 0-3-10 1-4 7-10-4 11-9-2 5 11 - 0 11-2 7 T-LEVEL FAMILY: 3-0/1/2: 0 1 2—0—2 0—2 1 MEASURE: 10,11 12 13 I T-LEVEL FAMILY: 3-0 3-1 3-2 T-LEVEL: 3 - 6 9 - 4 - 9 0 I OCCURRENCES: 7 5 5 I TOTAL TINE-SPANS 3-0/1/2: 0 1—0— 1 I8TH VALUES): 28 18 30 "II MEASURE: 1 2 3,4 5 6 7 8 9 10,11 12 T-LEVEL: 0 - 5 8 - 1 10 - 3 6 - 9 2 - 5 10 - 3 8 - 11-4 7 0-5 0 3-0/1/2: 0—2- 1- --1-- -0 —-2— 1—0- -2— 1 0—2--0 T-LEVEL FANILY: 3-0 3-1 3-2 OCCURRENCES: 7 4 5 TOTAL TINE-SPANS: 29 13 18 39 Figure 2-7 continued. "Ill" MEASURE: 12 3 4 5789 10 12 T-LEVEl: 0-5 8-3-7-10 1-4 7-0-5 8 11 2 6 9 2 5 0 3-0/1/2: 0—2——0—1 0—2 0 2 0 MEASURE: 13 14 I T-LEVEL FAMILY: 3-0 3-1 3-2 T-LEVEL: 5-0-4-70 1 OCCURRENCES: 624 I TOTAL TINE-SPANS 26.5 15 42.5 3-0/1/2: 2—0—1 0 I There are no clear consistencies in the locations and func• tions of the invariant diminished-seventh PCs of each T-level family, although with "I" there is a tendency for these PCs to be exposed in some sense (i.e., location in the outer voices, or exposure through temporal isolation). Such inconsistency cannot be explained by tonal procedures, such as resolutions of the two tritones comprising the invariant diminished-seventh structures (i.e., outward or inward semitonal resolution). Nor are there apparent consistencies in the locations and functions of the quasi-invariant PCs. In general, Fig. 2-7 illustrates the fact that 3-0 and 3-2 family T-levels each tend to occur more frequently and have to• tal time-spans greater than 3-1 family T-levels. Perle indicates that pivotal connections between harmonies in Trois Compositions are generally used "merely as a means of immediate association.""*2 This is generally true when "pivot" is defined as a pitch continuity in adjacent harmonies, since such pivot pitches generally exist between only two adjacent harmonies in Trois Compositions. On average, there is one pitch 90 continuity per succession, although there is constant fluctua• tion in the number o-f such pivot pitches with each succession. When "pivot" is understood more broadly as any invariant PC in adjacent harmonies, then there are more pivots as Ex. 2-17 has shown. The above-mentioned diminished-seventh -formations common to IC-3-related T-level families represent a more specific type of pivot reminiscent of Scriabin's Seventh Sonata., as analyzed by Perle. Another pivotal formation is the "diminished- seventh" chord, comprising the only notes common to all four members of the transpositional complex [i.e., the set at T-0, T-3, T-6, and T-93. ... Of importance in its connection with larger formal ele• ments is the group of notes comprising the tritone relationships within the set, the invariance of which at the transposition of a tritone results in a six- note segment common to any two sets a tritone apart."*»= While there is, on average, one pitch continuity per suc• cession, approximately 76% of such pivot pitches of Trois Com• positions (79% in "I", 77% in "II", and 73% in "III") are invar• iant diminished-seventh PCs of the T-level family to which ei- <• ther T-level of the given succession belongs. 91 Element Occurrence and Ordering in Trois Compositions Besides the study o-f T-level successions as to PC contents, there is the matter o-f vertical and linear element occurrence and ordering, both within individual harmonies and between adja• cent harmonies.'*'* Although Gojowy observes that only PC content o-f harmonically or linearly disposed collections (and not order• ing or registral location) is determined by the ICC system,'**9 there are identifiable, though limited, patterns of element oc• currence and ordering which will now be examined. Linear Element Occurrence and Ordering "I". Example 2-19 presents the pitches of the primary mel• ody of "I", with corresponding element numbers. Example 2-19. Primary melody of '" I' MEASURE! 1 I 2 13 |4 I 3 I T-LEVEU 0 10 I 1 I 7 10 4 | 11 9 2 | 5 | o Q ELEMENT* I I I II NUMBERS! 3 8 10 9 8 3 4 I 3 8 3 4 I 3 0 6 I 3 8 10 3 0 I 0 I 92 Example 2-19 continued. M. | 6 I 7 T- 111 I 11 fee. 1 ,i " Q—& 1 7 •# -4n g^bni^ L~— -TJ r*" OJL , \ u,\ n 5*^ VW<>.9 in r, o 1—"— NO.| 8 4 6 0 9 3 1 10 9 8 3 I 8 4 6 0 9 10 3 1 10 9 8 5 | N. | 8 I 10,11 | 12 | 13 T- I 7 13 6|949|0 E> Q\uW) \b0 I -t— NO.| 3 1 10 9 8 3|3 8 3 4 | 3 8 3 I 3 | Elements "3", "8", and "O" (in descending order o-f occur• rence) are used more -frequently in the primary melody, particu• larly in mm. 1-5 and 10-13. Where there are two or more primary melody pitches per harmony, one -finds that "3" and, to a lesser extent, "1", "8", and "9" occur -frequently as initial melodic elements. - In most cases, these elements represent the textural- ly isolated initial pitches o-f harmonies. Where there is only one melody pitch per harmony, elements "3" and "O" -frequently occur. Hencer element "3" would seem to be limitedly associated with this initiating -function. Elements "O", "4", and "8" -fre• quently succeed "3" in the primary melody. Element "O" also oc• curs in certain cadences (i.e., T-5, m. 5; T-O, m. 13; and T-10, m. 3) . 93 "II". Example 2-20 presents pitches o-f the primary melody of "II", with corresponding element numbers. Example 2-20. Primary melody o-f "II" K.| 1 12 | 3 I 4 I 5 I 6 I 7 18 | T-| 0 3 18 1 | 10 3 I 10 3 | 6 9 | 2 5 |10 3 18 11 4 | NO.I 11 8|8 4|8 4 I 11 9|3 3 I 3 0 11 1 3 0 11 | 3 0 11 31 H. I 9 I 10-11 I 12 I 13 I T-| 7 L 0 5 I 0| 0 1 N0.| 9 | 11 8 1 11 I 11 I Elements "11", "3", and "8" occur most -frequently in the primary melody, with element "11" the most significant o-f these as it is the initial element o-f the piece and o-f the recapitula• tion, and also the -final element. Moreover, the -final T-level (T-O, m. 13) is transposed in m. 6 (T-5, which succeeds f-2 and its pitch cl imax), m. 7 (T-3), and m. 8-.(T-ll), with el ement "11" retained in the primary melody in each case. However, there is no association with -function, as with element "3" in "I". There are no apparent patterns o-f element ordering within the primary melody. "III". Example 2-21 presents pitches pf the primary melody of "III",, with corresponding element numbers. 94 Example 2-21. Primary melody o-f "III". 12 |3 I 4 5 | 8 3 7 10 I 1 1 4|7 MM 3 9 10 6 8 9| 0 4 4 3 1 3 11 9 10 9 10 10 I 10 0 1 N. | 4 I 5-6 I 7 T- | 0 I 8 I 11 *\&9*<>"'' : N0.| 10 0 1 10 0 (8) I 6 (3) 10 I 8 3 0 1 4 6 13) 8 0 1 4 1 H. I 8 I 9 | 10-11 I 12 I 13 | 14-15 I T- | 2 6|9|2 13 15 0 4 7 10 I fee 3p MO.I U) 8 0 8 0 | 8 | 3 1 0 | 3 9 10 4 6 I 0 4 4 3 I 3 1 0 Although elements "O", "3", "4", and "IO" occur more fre• quently and have the greatest total time-spans, there is no ap• parent consistency in element recurrence or ordering. there are a number of element sequences that do recur, such as: »3»_»9»_ "10" in mm. 1 and 125 "O"-"4"-"4"-"3" in mm. 2 and 13; and "10"- "0"-"l" in m. 4. All three involve the transposition of harmon• ic-melodic figures, while sequences «3»-»9"-"10" "ll"-"9"-"10" (m. 3) involve no such repetition. Certain ele• ment recurrences suggest a limited form of element control: element "10" in m. 1, in m. 3 as a local melodic goal, in m. 4 as an initial element, and in mm. 5-6 as a melodic goal; and the 95 alternation o-f "8" and "O" in mm. 7-11. In the three pieces, elements "3", "0", and "8" occur most •frequently in the primary melody. Element occurrence in bass lines. In the bass lines, "1", "O", and "6" in "I", "4" and "6" in "II", and "1" and "6" in "III" occur most -frequently. In general, "1" and "6" occur most •frequently in the bass lines o-f the three pieces. Analyses o-f linear element successions involving adjacent harmonies reveal no consistent principles o-f ordering.419 Vertical Element Occurrence and Ordering in Individual Harmonies Limited patterns o-f vertical element occurrence and order• ing are, to some extent, significant despite any inconsisten- c i es. "I". Example 2-22a illustrates the PCs o-f the ICC at T-O, with Ex. 2-22b presenting the verticalized harmonies o-f "I" in sta-f-f notation and, below this, with pitches represented by ap• propriate element numbers. In the case o-f two or more primary melody pitches per harmony, the representative elements are sta• ted both linearly (i.e., on one line usually with dashes sepa• rating element numbers) and vertically. Brackets and asterisks highlight these verticalized melody pitches. Melody pitches in the score have stems that are connected to beams. 96 Example 2-22. Harmonies of "I" with pitches represented by element numbers. (a)PCs o-f ICC AT T-O: L„ ho ^ ELEMENTS: o 10 (b)Verticalized T-levels, with representative element numbers: "it ^ kg AN —^ gg-frg f VERTICAL POSITION 8 I §(10) 1 1 1 *(10> • 1 7 1 i(8) §8 0 1 4 0 1 9 6 0 1 i(8) «3 to 1 6 1 *3-8-10 3 8 1 *3 8 1 8 4 9 1 H-8-10 9 6 1 5 I 0 0 «(4) 1 0 *(4) 1 *3 M •6 1 0 1 9 1 4 1 9 V) 13-4 1 9 #3-4 1 0 8 1 1 9 0 3 1 3 1 4 i 9 1 *8 1 1 4 3 4 1 4 4 8 1 2 1 1 1 1 1 1 9 1 1 9 3 1 1 8 4 1 1 1 6 4 6 1 6 6 1 6 1 8 1 6 6 1 1 1 1 1 1 1 T-LEVEL: I 0 3 10 1 1 4 1 7 10 4 1 11 9 2 1 MEASURE: I 1 1 2 1 3 1 4 1 Jfre- \fnO P 8 1 1 I H0- 1 7 10 1 *9- 1 *9- 1 6 | 6 ••' 1 *0- 4 11 10 | *0- 4 11 10 I 3 1 4 Ml *8- 10 3 4 | *8- 10 3 4 1 4 1 1 * 1 *6- •13) *(10) »I8) | H- i(3) U10) *(8) | 3 | 8 4 | «4" *3-l *10-9 *8-3 | *4- *3-i *10-9 *8-5 | 2 1 3 1 1 (3) 11) (3) (3) I (3) (4) (1) (3) (3) | 1 1 9 (9-3-8) I 1,3 0,1 1,3 1,3 1 1,3-2,4 0,1 1,3 1,3 1 1 1 1 1 T- 1 3 1 11 0 1 11 2 1 N. | 3 1 6 1 7 1 97 Example 2-22 continued, 7 1 1 *3 9 1 8 •8 8 1 •0 1 4 1 4 11 10 | 0 •14) 1 •3 3 •3 1 6 1 SI 10 S 4|9 •3-4 1 0 0 0 1 3 1 4 1 •(3) •(10) •(8) | 18 1 1 9 9 9 1 1 1 3 1 •3-1 •10-9 •8-3 | 6 8 1 6 6 6 1 9 1 2 1 (0) (1) (3) | 1 6 1 1 4 1 1 8 1 1 1 11,0 0,1 1,3 1 4 0 1 4 1 4 1 3 1 1 1 1 1 1 T- 1 7 1 3 6 1 9 4 9 1 0 1 N. 1 8 1 10,11 1 12 1 13 1 Note: Asterisks (*) indicate primary melody elements, while "+" (m. 4, T-9 and T-2) indicates a simplification in the represen• tation of these sonorities whereby melody elements "3" and "0", respectively, doubled one octave below, are deleted in order to show the seven-element sonority. "++" (m. 5, T-5) shows an al• ternate way o-f regarding the lower pitches o-f T-5 harmony, as melodic approach pitches to Eb4. In Ex. 2-22 and those to -follow, the lowest vertical posi• tion in a chord (i.e., the lowest pitch) is designated "position one," the next lowest position "position two," and so on. Hence, the first harmony of "I" (Ex. 2-22) has element "6" in position one, "1" in position two, "4" in three, "9" in four, and so on. Because seven-PC harmonies consistently appear, es• pecially in mm. 1-5 and 10-13, certain patterns of element oc• currence in the individual vertical positions can be observed, as illustrated in Figure 2-8. 98 Figure 2-8. Element occurrences in vertical positions of the harmonies o-f "I". (a) Most -frequent element (b)Most frequent element occurrences in positions occurrences in position in " I " : ranges in "I" : E1ements Position | Elements ranges I 4- 8: I 0, 3 8, 9 4, IO 7: 0,*8 9 I 6: 3 4 1-3: I 14 6 3 5: *0 4 I 4: *9 3,8 1 I 3: *4 6 5- 8: I O 3 4 8 9 2: *1 *3 8,9 I 1: 1 *6 i-3: I 1 3 4,6,9 8 0,4 Note: In proceeding -from left to right in Fig. 2-8a and 2-8b, there is a descending order o-f element frequency in a position or position range. A comma between two elements (e.g., 0,4) indicates that elements "O" and "4" occur the same number of times in a certain position. "#" indicates the most frequent occurrences of an element in any position. Patterns of vertical element occurrence in ranges of verti• cal positions (Fig. 2-Sb) have elements "1", and, to a lesser extent, "3", "4", and "6" as occurring frequently in the lower positions of harmonies, while elements "0", and, to a lesser ex• tent, "3", "4", "8", and "9" occur more frequently in the upper posi t ions. However, as shown in Figure 2-Sa, a different element is generally the most frequently occurring in each vertical posi• tion, except for positions one and two, in both of which element "1" is most frequent. If we substitute the next most frequent element, "6", for "1" in position one, we obtain a "referential" harmony -for "I", in the sense that it reflects the average reg• istral distribution of the elements of the PCC. That is, many 99 o-f the harmonies in "I", especially in mm. 1-5 and 10-13, are variations o-f this " re-f erent i al " structure. It consists o-f ele• ments »6•,-',l,'-"4,,-"9,,-•,0"-"3"-,,8,, , ordered -from lowest to high• est in register. When we substitute T-O PCs -for these elements, this "referential" harmony is Ab-Eb-Gb-Cb-D-F-Bb, the -first ver- ticality o-f "I". In other words, the -first vertical ity o-f "I" establishes a normative registral distribution o-f elements o-f the PCC, a distribution which is maintained, statistically, throughout "I". This statistical uniformity is not maintained in mm. 6-8 due to the use o-f the expanded ICC, and the textural d i fferences. "II". The patterns o-f vertical element occurrence are il• lustrated in Ex. 2-23. lOO Example 2-23. Harmonies o-f "II" with pitches represented by element numbers. (a)PCs o-f the ICC at T-O: bo 9 ELEMENTS: o 1 11 (b)Verticalized T-levels, with representative element numbers: VERTICAL 8 1 1 i 1 1 1 3 1 POSITION 7 1 11 8 1 8 4 1 8 « 1 11 9 1 «3 t3 | 11 U 1 6 1 8 11 1 11 11 I 11 9 13 4|9 6| 11 8 8 8 | 3 1 0 9 1 6 6 1 9 3 19 11 I 6 11 | 8 3 0 0 1 4 1 0 6 1 4 0 I 6 11 18 3 I 11 8 1 0 11 9 6 1 3 1 6 4 1 0 8 |06 10 6 14 0| 4 6 3 1 2 1 4 0 1 3 9 13 8 16 8 10 9| 9 4 9 1 11 9 3 1 9 3 1 4 0 14 0 18 4| 6 tl t4 1 t4 I 1 1 1 III • 1 T-LEVEL 1 0 3 1 8 1 I 10 3 1 10 3 1 6 9 | 10 3 1 MEASURE 1 1 1 2 1 3 14 15 | 6 1 it 5E r IS fe—I ^ ho. 7* 3 E JZL ~0~ — 7 1 3 0 11 1 3 0 11 3 1 9 1 11 8 1 U 1 11 1 6 1 11 8 8 1 11 8 8 8 1 3 1 8 U 1 8 1 8 1 5 1 8 3 0 1 8 3 0 6 1 0 1 3 9 1 9 1 0 1 4 1 0 11 6 1 0 11 6 4 1 6 1 0 6 1 0 1 6 1 3 1 4 3 1 4 3 0 1 4 1 9 3 1 9 1 3 1 2 1 9 9 1 9 9 9 1 11 1 4 0 1 4 1 9 1 1 1 6 tl t4 t4 | 6 tl t4 t4 til | t8 | 6 4 1 6 1 t4 | 1 1 - 1 1 1 1 1 T- 1 10 3 1 8 4 1 7 1 0 51 0 1 01 N. 1 7 1 8 1 9 1 10-11 I 12 I 13 I lOl Note: Asterisks (#) indicate deleted doublings o-f primary melo• dy and bass elements, simplifications of harmonies in order to show the seven-element sonority. "+" (m. 6) indicates a modifi• cation of the T-2 harmony, with all elements including "1" in the vertical representation. Unlike the harmonies of "I", those of "II" always have the primary melody element in the uppermost vertical position. With regard to element occurrence in ranges of positions (lower three positions and the upper four, as suggested by the duple-triple polyrhythmic figures of mm. 1-5 and 10-13), elements "4" and, to a lesser extent, "9", "6", and "O" (F, Bb, G and Ctt, respective• ly)**5* occur frequently in the lower three positions while "8", "11", and "3" (A, C, and E, respectively) occur frequently in the upper four positions. As with "I", a "referential" harmony of "II" can be derived from the frequently occurring elements (from lowest to highest, » .. 4 _M9»_.,3.._»6.. _..on_n8»_n X1 n ) _ Like the "referential" harmony of "I", this structure actually occurs in "II", in mm. 13 (T-O), 6 (T-5), 7 (T-3), and 8 (T-ll). "III''. Because of the variable texture of "III", in the number of elements per harmony, and in the contrapuntal inner voice fragments, the harmonic structures are not consistent. However, Ex. 2-24 attempts to interpret the music similar to Exx. 2-22 and 2-23. Elements within one T-level or harmony that can be interpreted as melodic (especially those separated by a semitone or tone from adjacent elements) are included in Ex. 2- 24 with the adjacent element(s) in one position, but these are also verticalized so that only one element occurs in one posi- 102 t i on, Example 2-24, Harmonies o+ "III with pitches represented by element numbers. (a)PCs o-f the ICC at T-0: bo n o bo \\o X o ELERENTS: 10 11 (b)Verticalized T-levels, with representative element numbers VERTICAL 10 POSITION 9 | T-LEVEL MEASURE 103 Example 2-24 continued. lip 3g -*e- i 2 iZ2I 10 1 HO-0 | 1 1 9 1 8 1 1 1 8 1 0—1 I 1 §3- 3 1 71 I10--0--1—10—0—1 - 9 1 3 1 *8- 0 1 61 8--6 8-6 4 | 8 1 #4- 4 1 *8--0--8 SI 0--1--0 0-1-0 10 I 4 1 §0-1- 1 1 3 8 0 4 1 9 8-9 9 9 tt 1 0 1 *6— 8- | 0 4 6 3 1 4 - 4 — 3 1 •10 1 *0-l- | 6 3 4 2 1 10 8 10 1 •6-10 | 1 4 6 3 1 1 8 10 8 I 1 1 Ml 1- 1 1 1 1 T- 1 7 0 3 1 8 1 11 1 2 M. 1 4 1 3-6 1 7 1 8 io i i I I » I 9 1 I I I M-6 | I I *3-9~10 11 I 8 1 I 4 71 M I «8 I *10 8 4 | tO 6| 8| 0 I M I *9 3 I 1 6 | 8 S| 3| 3 18 I 4 0 4 1 4| 6 I *3~l-0 | 0 8 I 6 »3 I 13--1- 3 1 6 | 10 I *1 I 8 6 I tO M *4 0 | tl 2 | 10 | 4- -3 14 I 6 11 I 4 13 8 14 II 1 1-0-11 I I 1 2 I 16 0 1| 6 I I I I I T-1 6|9 I 2 I S I 5 0 4 7 | 0 •.1819 I 10-11 I 12 13 I 14-13 104 A study of element occurrence in lower and upper ranges o-f positions reveals a tendency -for elements "1", "4", and "6" (G#, B, and Db) to appear more -frequently in lower vertical posi• tions, and "0", "3", and "8" Elements "2", "5", "9", "10", and "11" do not appear as consistently as elements "0", "1", "3", "4", "6", and "8", the invariant or unbracketed elements o-f the ICC. Patterns of ele• ment occurrence in individual positions are such that often two and more elements are strongly represented in one position; hence, there is no clear "referential" harmony. "I", "II", and "III'' as a whole. There are no apparent consistencies in vertical element location and occurrence in the three pieces as a whole. As suggested by the "referential" har• monies of "I" (elements "6"-"1"-"4"-"9"-"0"-"3"-"8", lowest to highest registers) and "II" ("4"-"9"-"3"-"6"-"0"-"8"-"11"), ver• tical element distributions in harmonies of the two pieces tend to be quite different. With "III", there is no "referential" harmony, although a few harmonies bear some resemblance to those of "I". Figure 2-9 illustrates limited tendencies in ranges of vertical element positions in the three pieces as a whole. 105 Figure 2-9. Vertical element occurrence in ranges o+ positions in Trois Compos i t i ons. Groups o-f Frequently occurring elements (descending order o-f vert i cal frequency; elements with fewer occurrences in pos i t ions: brackets): 4- 7 O, 3, 8, 9 (4, 9, 11) 1-3 4, 1, 6 (8, 0, 9) 5- 7 8, 3, O (4, 9, 11) 1-4 6, 4, 1, 0 (8, 9, 3) Elements "1", "4", and "6" (Eb, Gb, and Ab) tend to occur in the lower three or four vertical positions while "0", "3", "8", and "9" Vertical Element Adjacencies Element adjacencies, which are independent of vertical po• sition, likewise have no consistencies indicative of deliberate PC control. There are however a few identifiable adjacencies (e.g., elements-pairs, and e1ement-trichords) occurring with enough frequency to be of interest. What is particularly note• worthy is the fact that the vertical element orderings of many of the harmonies in each of the pieces (especially in "I" and "II") appear to be derived from a limited number of vertical element structures in the respective pieces. Derivation is pri• marily through rearrangements of element-pairs and -trichords, and inversions of elements within these pairs and trichords. This would suggest that elements, and not just PCs, are an im• portant determinant in vertical element ordering. Example 2-25 illustrates such a process of derivation with the harmonies of 106 Example 2-25. Similarities o-f harmonies in "I" (with pitches represented by element numbers). I 10 I 0 0 4 1 I 8 I 8 1 8 8 8 3 |8 I 3 I I 3 I 3 I I 0 0|0 I 0 I » I 9 9 I 9 I 9 I I 8 I I I 4 I 4 I 4 I 4 I 1 I 1 1 I 1 I 1 I 6 I 6 6 I 6 I 6 I I I T-LEVEL | 0,11 7 3, 9 4 3 I 0 io 1 I 0 0 I 0 MEASURE | 1,4 3 1,12 12 10,11 |1 1 2 2|1 I 1 a? £3£ te l 0 0 0 1 6 I I 3 6 6 6 |9 9 4 | I 9 0 0 |3 4 I I (3) 9 9 4 1 8 3 0 I 4 11 10 4 11 10 I 1 3 3 110 8 | 10 3 4 10 5 4 I 0 8 I 1 I 3 10 3 10 I 4 8 9 14 8 3 | (1) 9 1 9 I 8 4 4 3 | 1 6 9 I 1 3 0 1 16 118 16 0 1 I 0 1 1 11 0 I I I T-LEVEL | 9 2 2 3 1(0) 6 11 10 | 0, 2 7 MEASURE | 4 4 4 5 1(1) 10,11 6,7 3 I 6, 7 8 107 Note: In this and following Examples dealing with vertical ele• ment adjacencies, gaps in the vertical presentations of elements are for the purpose of highlighting vertically adjacent elements used in other harmonies. T-O (m. 1) is restated for purposes of compar i son. Many of the harmonies are clearly derived from T-0, m. 1, which explains the resemblance between the "referential" harmony and the T-O harmony of m. 1. However, the derivation of some harmonies require explanation. T-l (m. 2) is the same as T-O (m. 1) except for an exchange of "4" and "8". T-10 (upper position elements) are interpolated with »6"-"4"-"l" to produce "6"-"8"-"4"-"0"-"1", with «9»-»3» in the upper two posi• tions. Likewise, T-6 (mm. 10-11) involves a similar alternation of elements. Although T-2 (m. 4) and T-5 (m. 5) do not readily resemble element formations of other harmonies, T-2 is derived from T-5, with the vertical rearrangement of element-pairs and an e1ement-trichord. The harmonies of mm. 6-8 do not appear to have been derived from other harmonies in the piece, but these measures comprise a distinct formal section with different har• monic structures based on an expanded ICC. However, one harmony which has limited similarities to the final harmonies of mm. 6, 7, and 8 is T-O (m. 13), which shares elements "1", "3", "4", and "8" with this final harmony. Similar methods of element reordering are used to illu- 108 strate the derivation of some harmonies in "II" (Ex. 2-26). Example 2-26. Similarities o-f harmonies in "II" (with pitch* represented by element numbers). I I 11 8 I 11 I 8 11 8 I 11 11 3 11 8 I 8 8 11 3 9 11 I 3 3 8 9 9 I 0 0 0 11 6 6 4 3 0 9 0 3 6--1--4 9 3 4 4 I T-LEVEL | 0 0 2,10,8 3,3,11,0 | 0 3 3 10 MEASURE | 1 10-12 6, 7,8 6,7,8,13 I 1 1 10,11 3 109 Example 2-26 continued. I 11 8 8 11 I 8 11 3 0 I 8 11 4 11 4 I 1 3 11 8 11 11 9 61 3 6 8 0 I 8 11 0 3 3 1 6 I 0 8 0 11 I 3 1 9| 3 6 9 19 9 3 4 1 4 4 6—1—4 I T-LEVEL | 0 8 1 0 3 3 | 10 10 10 MEASURE | 1 2 2 1 3 7 13 4 7 110 Example 2-26 continued. £3iif* c I3 1 11 3 1 11 11 1 1 4 3 3| 3 6 1 8 9 3 1 1 11 9 6 | 9 8 1 3 8 8 1 1 6 U 1 6 0 11 1 3 0 1 1 6 I 1 0 6 1 1 0 11 8 | 11 6 81 0 6 4 6 1 1 8 4 0 | 4 3 0 1 6 4 0 3 1 1 9 1 4 1 1 9 0 9 | 0 9 1 11 9 9 1 1 3 8 4| 8 4 4 1 9 8 11 4 1 1 1 1 1 1 6 9 | 6 11 9 1 0 7 4 11 1 1 2 3 3 | 3 8 3 | 10 9 8 8 1 The ascending order o-f elements in T-l extraction -from T-5 ing order. This process o-f extraction includes rotation through the element order, in the sense that once the uppermost element or next to uppermost element o-f the harmony's ascending order has been used, one proceeds to the next-lowest or lowest ele• ment, respectively, o-f the harmony to extract the next element in the order. Similarly, the descending order o-f T-ll's lower elements Unlike those o-f "I" and "II", many o-f the harmonies o-f "III" are not clearly derived -from element reorderings o-f other harmonies. Example 2-27 illustrates those harmonies with similarities in vertical element adjacency. Example 2-27. Similarities in the harmonies o-f "III" (with pitches represented by element numbers). I 4 1 I 1 0 4 8 1 6 3 8 4 18 0 8 0 1 4 1 3 3 1 3 8 1 6 13 8 0 8 1 1 6 0 1 1 8 0 6 3|0 3 3 3 1 6 8 1 1 4 6 1 3 4 | 0 4 4 0 16 6 10 1 1 3 8 1 6 1 4 1 3 8 14 10 4 4 1 8 0 6 0 1 1 6 0 111 1 1 6 1 1 1 1 8 3 7 10 I 5 0 4 7|2 6 9 2,0 1 2 2 2 2 1 13 13 13 13 | 8 8 9 10,14 112 Example 2-27 continued. 1 3 0 8| 0 6 1 4 3 1 4 81 1 1 8 8 0| 4 3 1 1 8 1 3 1 1 3 4 0 1 1 4 3 3 1 1 8 1 6 0 1 0 6 1 8 6 8 1 1 0 4 6 1 1 1 1 1 3 3 1 1 10 6 10 I 6 0 1 3 4 1 8 4 1 4 0 1 1 1 6 10 4 I 3 4 1 8 I 1 1 3 1 6 8 4 1 1 1 1 H 8 1 1 0 6 1 6 0 1 0 1 6 1 1 1 1 1 1 1 T-LEVEL | 8 6 91 8 3 1 3 0 1 7 4 1 10 7 0 i MEASURE | 3-6 8 9 1 2 13 I 2 13 I 2 13 I 2 13 14 1 In general, the vertical element orderings o-f harmonies in "III" are such that -fewer chords are derived -from preceding chords. This constrasts to some degree with the harmonies o-f "I", many.o-f which are derived in some recognizable extent -from preceding harmonies, particularly T-O, m. 1. In -fact, there are certain similarities between the chord structures o-f "I" and "III", because o-f the common element content (i.e., »0"-"l"-"3"- "4"-"6"-"8") o-f their respective ICCs, as shown in Ex. 2-28. As many o-f the harmonies in "I" are derived -from T-O (m. 1) , this will be the only harmony o-f "I" cited in the comparison with structures o-f "III". 113 Example 2-2S. Similarities in vertical element orderings of harmonies in "I" and "III". 1 8 1 1 1 (0) 1 1 1 10 (8) 1 1 3 1 8 (6) 1 10 0 1 9 11 1 3 0 3 (4) 1 3 9 8 1 4 10 1 0 8 8 3 1 8 8 3 1 3 9 1 9 3 0 0 1 1 4 6 1 1 8 1 4 1 4 6 1 4 6 4 1 8 1 1 1 4 1 4 1 6 0 10 I 6 0 1 6 6 6 1 1 0 1 1 1 0 6 1 1 1 T-LEVEL 1 0 2,0 0 2 1 10 1 6 1 6 1 MEASURE 1 1 10,14 13 8 1 2 3 8 1 10,11 3 1 1 3 3 3 1 3 3 3 1 1 3 Such vertical adjacencies and derivations o-f harmonies by element reorderings o-f preceding harmonies may well be typical o-f Ros 1 avets's music. Cone 1us i on Having examined the ICC system in Trois Compositions and characteristics that pertain to its application in the music, we should summarize some of the important points raised in this chapter. Each piece's harmonic organization is based in part on the ICC associated with the given piece, the ICC whose PC content is transposed to produce the PC collections comprising a piece, usually expressed harmonically but at times linearly. Although there is a basic ICC -for each piece, and each PC collection rep• resents a transposition o-f that basic ICC, there are variations in element content. Interestingly, though the PC content o-f the three basic ICCs differs, there are important similarities in element contents In each piece, one T-level (T-O) acts as a referential son• ority -for the given piece, in the sense that the sonority begins and concludes the piece and is most significant in that respect and as to frequent occurrence, greater total time-span through the piece, and coincidence with formally important time-points. T-levels can in fact be hierarchized, based on these criteria, indicating the significance of each in a given piece. Each piece has a different hierarchy of T-levels, although T-0, T-5, T-3, and T-8 are significant T-levels in the three pieces as a who 1e. Harmonic successions generally involve IC-3- and IC-5-rela- ted T-levels, and frequently employ two, three, and four compon• ent T-levels of an ascending interval 3 or 5 cycle, or combina• tions thereof. Especially in "I" and "III", three or four T- levels of an interval 3 T-level family in cyclic order (e.g., with the 3-0 cycle, T-O,T-3,T-6,T-9) are employed before pro• ceeding to another interval 3 cycle or component(s) thereof. However, a number of the transferences from one interval 3 T- level family lor component) to another involve IC-5-related T- levels. In fact, in "II", as opposed to "I" and "III", the harmonic succession is based on a reordered interval 5 cycle. PC invariance in all four (or even three or two) T-levels of a family of IC-3-related T-levels and transferences from one family (or component) to another may be viewed as analogous to the PC collection of a tonal key and modulations between such keys. 115 Studies of PC and element occurrence, ordering, and associ• ation, within individual PC collections and involving adjacent collections, show no readily apparent consistencies indicative 0- f deliberate control o-f PC organization. Because most harmonic successions involve IC-3- or IC-5-related T-levels, there are usually three or -four invariant PCs in a given succession, while only one o-f these invariant PCs involves pitch continuity. IC- 1- , -2-, -4-, and -6-related T-levels, which occur infrequently in all three pieces, have fewer invariant PCs. Pitches tend to proceed by IC-1 and -2, somewhat less by IC-3 and -4, and much less by IC-5, and -6, to those pitches of succeeding harmonies in the same voice or vertical position, with no apparent, con• sistently applied principles of voice-1eading or pitch succes- s i on. Elements "3", "0", and "8" tend to occur most frequently in the primary melodies of the three pieces, with "3" in "I" (as to its occurrence as initial element of most T-levels) and "11" in "II" having added significance. Elements "1" and "6" occur most frequently in the bass-lines of the three pieces.4- In general however, few apparent consistencies in element ordering are found in the melodies and bass-lines of "II" and even moreso in "III". Some significant patterns of vertical element occurrence, ordering, and association are to be found, especially in "I" and "II". In the three pieces as a whole, elements "1", "4", and "6" tend to occur in the lower register, "0", "3", "8", and "9" in the upper. "Referential" harmonies of "I" and "II" consist 116 of the most frequently occurring element in particular vertical placements. Many harmonies in "I" and "II" represent modifica• tions of the respective "referential" harmonies. The study of vertical element adjacencies (i.e., element-pairs and -tri• chords), and the derivations of element orderings of many harmo• nies from those of a few, bear this out to some extent. Such derivations are through the following means: rearrangements of element-pairs and -trichords; inversions of elements within these pairs and trichords; rotations upward and/or downward; the derivation of alternate elements of one chord (in one direction or another) to produce the element ordering of another; and sym• metrical reorderings of elements. This suggests that elements, and not just PCs, are a determinant in vertical ordering. Many of the harmonies in fact involve some recognizable, minimal modification of the element ordering of others. With "I" and "II", there is a certain homogeneity of element order in the harmonies, much less true of "III". In general, there are certain stylistic characteristics that differentiate "I" and "II" from "III", the more salient of these being: (1) the PC contents and ICAs of the ICCs, and the use of more variant T-levels in "III", indicative of freer ap• plications of the ICC system in the last piece; (2) the greater flexibility in harmonic rhythm in "III", specifically the in• consistency in T-level time-spans, compared with the harmonic rhythms of "I" and "II"; (3) the more pervasive use of complete, uninterrupted ascending interval 3 cycles of T-levels in "III" as compared with "I"; (4) fewer identifiable patterns of PC and 117 element occurrence, ordering, and association in "III", due in part to the variances in texture, and the tendencies toward lin• ear, contrapuntal activity; and <5) fewer, overtly tonal struc• tures and procedures in "III", which is made evident in Chapter Three. However, there are certain similarities between "I" and "III" that perhaps suggest a recapitulative ternary structure relating the three pieces as a set. Such a structure in -fact imitates the recapitulative ternary -form o-f each piece. These similarities are: (1) the use o-f complete interval 3 cycles o-f T-levels in "I" and "III", as opposed to the use o-f the interval 5 cycle which characterizes "II"; (2) both "I" and "III" have portions o-f their development sections (mm. 6-8, and m. 4, res• pectively), employing successions -from the interval 5 cycle; (3) the general irregularity o-f the harmonic rhythm, as opposed to that o-f "II"; (4) the tendency to have elements "1", "4", and "6" in the lower range o-f vertical positions, with "0", "3", "8", and "9" in the upper range; and (5) the procedure o-f sub• dividing PC contents o-f a T-level to produce contrasting harmon• ic content in mm. 6-8 o-f "I" (specifically, T-O, T-2, and T-7) and m. 4 o-f "III" (T-7, T-O, and T-5). Notes 1. Gojowy, Meue sowjetische Musik, 138 (my translation). 2. Gojowy, "Hal-f Time," 212. 3. Perle, Serial Composition, 43. 4. Gojowy, Neue sowjetische Musik, 138. 118 5. Wallace Berry de-fines a pitch-class (PC) as "pitch inde• pendent o-f specific registral occurrence" and pitch-class-com• plex (PCC) as "a complex o-f such pitches generically under• stood." (Wallace Berry, Structural Functions in Music CEnglewood Cli-f-fs, New Jersey: Prentice-Hall, 19763, 27n. ) 6. Although the PCs o-f a T-level can be expressed linearly in the music, as they are to some degree in "I" (T-ll, mm. 6 and 7) and "III" (T-ll, m. 7), a T-level in Trois Compositions usu• ally occurs in the music as a single harmonic unit with certain melodic components (i.e., pitches o-f the primary melody, bass line, or inner melodies). "Primary melody" refers to a linear pitch continuity usually -found in the upper voice of a piece, although it may appear for a time elsewhere in the texture. Such a placement in the uppermost part of the texture, in con• trast to other linear pitch continuities found in inner voices or those forming a bass line, focuses one's attention on it; hence the primacy of this melody. The "bass line" is the se• quence of pitches formed by the lowest pitches of harmonies, usually one for each harmony. 7. Perle, Serial Composition, 43; Gojowy, Neue sowjetische Musik, 138-141. However, Gojowy does not apparently explain the method of segmentation into pitch collections used to arrive at these T-level successions. In Gojowy's notational system, which is used for his charts that identify the ICCs and their PC con• tents in musical excerpts, the twelve-PC system (i.e., PCs of a chromatic scale beginning with C) is used. PCs of the ICC, in ascending scale form, are represented by X's, while those PCs not of the ICC are represented by O's. Hence, the ICC of "I" is represented by the following: 0-0-X-X-O-X-X-O-X-O-X-X. Gojowy also represents this ICC with a short-hand designation XII=1,2, 5,8,IO, where an ICC based on a 12-PC system (XII) lacks ele• ments 1(C), 2(C#/Db>, 5(E), 8(G), and 10(A). In notating the ICC T-levels, Gojowy uses a designation very similar to that used by Perle; namely, "TI" to represent the initial appearance of the PCC in the piece, "T2" as this PCC transposed up a semi• tone, and so on. In my study, as in Perle's, the initial PCC will be referred to as the "T-O" level. 3. More specific guidelines of segmentation should be es• tablished. One principle is to isolate simultaneities and de• lineate pitch collections using time-points where there are in• terruptions in pitch activity in all voices or parts. In other words, one groups together into single collections those pitches whose time-spans overlap. While not prohibiting the inclusion of single pitches into two adjacent T-levels, this initial prin• ciple makes that less likely while allowing most pitches that are temporally associated to be included in the same collection. Then, and especially when there is consistency in the number of PCs per collection, these segmented collections are examined for PC and IC similarities. Combining smaller collections into lar• ger ones or dividing collections into subsets in order to main- 119 tain consistency of collection size, is another principle in de• termining the derivation of harmonies from ICCs in Roslavets's music. There are a few exceptions to the above-mentioned guide• lines of PC segmentation. In m. 3, the three harmonies (T-7, T- lO, and T-4) would otherwise be considered as one, because of the sustained C4 and the guidelines indicating that overlapping pitches are included in a single ICC T-level. The consistent occurrence of six to eight PCs per harmony, often as simultanei• ties, is the criterion for designating three harmonies in m. 3. Although the second halves of mm. 6 and 7, and m. 8, would ap• pear to represent a situation similar to that of m. 3 (whereby these time-spans, despite the trills, are segmented into three harmonies), a different approach is employed in assessing the segmenting of these time-spans, as discussed later in this sec• tion of Chapter Two. 9. Allen Forte, The Structure of Atonal Music (New Haven, Connecticut: Yale University Press, 1973), 13f. 10. Berry defines an interval class (IC) as including "any given interval within the octave together with its inversion (complement) and all compound extensions (expansions by one or more octaves) of the given interval or its inversion. If enhar- monically equivalent forms are considered of the same class, there are six interval classes (the unison excluded). ..." (Berry, Structural Functions, 193n.) 11. To reiterate, each ordered PC is numbered according to the PC interval it forms with the first PC of the collection. 12. Elements (i.e., the PCs in specific positions within the ICC scale form) have numbers in quotation marks (e.g., "0") in the text of the thesis to distinguish these from other arabic numbers. Again, element "O" in an ICC or its T-level would rep• resent the "first" PC although "first" does not imply primacy or importance as of the first degree of a tonal scale. 13. Gojowy, "Half Time," 212. Elsewhere, Gojowy refers to "scale-defined tone-complexes", with specific intervallic rela• tionships between the component PCs. (Gojowy, Neue sowjetische Musik, 138.) 14. Perle, Serial Composition, 43. 15. Ibid., 44. 16. See fn. 8 for principles underlying segmentation of pitches into PC collections. 17. Perle, Serial Composition, 43. 18. In thinking ahead to the discussion of "III" and to Gojowy's analysis of ICC structure (he identifies four similar but individual ICCs), one wonders why he indicates that four 120 ICCs are operative in "III" while only one is operative in "I", this despite the fact that the original ICC of "I" does not eas• ily explain the PC collections of mm. 6-8. Another approach to T-level identity in mm. 6-8 is to base each of the three harmo• nies in the three aforementioned time-spans on an ICC T-level most closely resembling the PC content of the harmony in ques• tion. This is examined in more detail in Appendix B. 19. Gojowy, Neue sowjetisc/?e Musik, 138-139. 20. Ibid., 139. 21. Interestingly, in Gojowy*s listing of T-level succes• sions, there is an "X" in m. 7 which is likely meant to desig• nate the T-level with element "1" although this particular vari• ation also occurs in mm. 6 and 8 (which have no "x" in Gojowy's 1i st i ng) . 22. That is, element "1" pitches occur a perfect fourth (IC-5) below the initial bass pitch, as the fifth of the minor- minor-seventh chord that constitutes the lower component of these harmonies. In a sense, element "1" has strong tonal im- p1icat ion. 23. Gojowy, Neue sowjetische Musik, 139. 24. Ibid., 141. 25. Perle, Serial Compos i t i on, 43-44. A recent article by Perle prompted an examination of "III" in terms of its musical orthography. (Perle, "Scriabin's Se1f-Analyses," Music Analysis, 3/2 CJuly 19843: 101-124? especially 107, llO-lil.) Such con• stancy in the intervals formed between ordered (scale form) PCs of T-levels in "III" undoubtedly led Perle to suggest the use by Roslavets of a single ICC. Quite likely although unsubstanti• ated is the fact that Roslavets may have been influenced by Scriabin in this regard. Although the ICC of "III" is noted be• cause of its different PC interval pattern, those of "I" and "II" are similar in the sense that the respective T-levels con• sistently reflect the PC interval pattern of the particular piece's ICC. 26. Perle indicates the practice of element omission but the illustration of the ICC or "set" of "III" fails to bracket PC Bb (i.e., element "3" in ICC at T-O) as such a variant ele• ment. (Perle, Serial Composition, 43-44.) 27. Another approach to T-level identity in the three pieces, given the similarities of the three ICCs, is to have one single ICC for all three pieces. This is briefly examined in Appendix B. 28. Gojowy, Neue sowjetische Musik, 140 (my translation). 121 29. Later studies of PC invariance in IC-3-related T-levels will group such T-levels into T-level -families (i.e., with T- level -family 3-0 including T-0, T-3, T-6, and T-9, and 3-1 and 3-2 -families including T-levels corresponding to those in the 3-1 and 3-2 cycles, respectively). 30. The reasons -for these displacements would seem to be related to the tonal aspects o-f the piece, which will be dealt with in Chapter Three. The T-10,T-3 succession, reiterated in mm. 3-4 (which in itsel-f is significant), has an Eb-major triad PC component which is generally invariant through these mea• sures. The T-ll,T-4 succession (m. 8) similarly has an E-major PC component which is invariant in mm. 8-9. Both o-f these tri• ads have important structural implications -for and relationships with the apparent "tonality" o-f "II", F major. 31. If T-level designations were altered so as to reflect the use of one ICC for all three pieces, there would be no con• nections between the cyclic T-level successions of the three pieces, in terms of some structure involving all three. Such T- level successions appear to be independent of one another. 32. Berry, Structural functions, 27. 33. This is done in order to provide a more realistic eval• uation of T-level significance in the event that a T-level oc• curs frequently but has relatively short time-spans, or with the opposite situation. 34. Perle, Serial Composition, 43. 35. Interestingly, T-ll in "I" (mm. 6 and 7) and in "III" (m. 7) both involve linearizations of the T-level PCs. 36. Both T-5 and T-7, IC-5-related to T-O, have a somewhat symmetrical or "opposing" relationship. The tonal analogies as• sociated with T-O (tonic?), T-5 (subdominant?) and T-7 (domin• ant?) will be examined in Chapter Three. 37. Perle, Serial Composition, 43. 38. Allen Forte, The Structure of Atonal Music, 29f., especially 31-32. 39. PC invariance and pitch continuity as pertaining to prolonged T-levels is discussed in Appendix B. 40. T-levels T-1, T-4, T-7, and T-10 are part of T-level family 3-lj T-levels T-2, T-5, T-8, and T-ll, part of T-level family 3-2. 41. With T-level families of "I" and "III", these invariant and "quasi-invariant" PCs form octatonic 1-2 (i.e., semitone- tone) collections while such a PC collection derived from T- 122 level -families o-f "II" -forms an octatonic 2-1 (i.e., tone-semi• tone) collection. In a recent article on the development of oc- tatonicism in Russian and non-Russian music, Richard Taruskin has some interesting observations concerning the octatonic col• lection in the music o-f Scriabin that have some implications -for the music o-f Roslavets. He states that in "the music of his CScriabin'sl last period, . . . the octatonic collection does not interact with diatonic harmony or emphasize triadic cog• nates. . . . Rather, in a work like the Sixth Sonata, Op. 62 (1911-12) . . . the three octatonic sets act as referential col• lections, -functionally akin to keys in the traditional sense. ... A sense o-f tonal motion is achieved by modulations from one octatonic grouping to another. That this was a con• scious technique based on traditional tonal procedures is made clear by the fact that a Scriabin essay in octatonicism, what• ever the vagaries along the way, will always end in the same oc• tatonic key as it began. That Scriabin conceptualized the octa• tonic collection as a pair of intercalated diminished-seventh collections ... is revealed by his note spelling. ..." (Richard Taruskin, "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'," Journal of the American Musicological Society, 38/1 CSpring 19853: p. 99, fn. 47). In the case of the three individual pieces by Roslavets, the three octatonic col• lections are derived from the invariant and "quasi-invariant" PCs of 3-0, 3-1, and 3-2 T-level families, respectively. More• over, transference from one octatonic collection to another, or, in other words, from one T-level family to another, whether a T- level family is represented by one or by more T-levels (as is the case with the three pieces, where series of T-levels ascend• ing by IC 3 are common). With regard to the final cadence, Roslavets not only concludes with the same T-level family with which the piece begins, but ends with the same T-level. Of course, similarities in the usage of octatonic techniques by Scriabin and Roslavets may be limited because of such things as the PCs in a T-level family which occur with only one T-level. (There is no readily apparent pattern to the location or func• tion of these "non-octatonic" PCs in Trois Compositions. Hence, the octatonic system as applied to the pieces is primarily theo• retical in nature, and is not indicated in PC events.) There are situations in the three pieces (as will be demonstrated in the discussion of tonality in Chapter Three) where tertian tonal structures and tonal procedures are employed, which differ from Scriabin's practice of non-interaction between the octatonic collection and tonal structures. Yet, despite such differences in the form of octatonicism in the music of Roslavets, there may be some basis for the application of octatonic theory and struc• tures to the music of Roslavets, if not to the three pieces. In Chapter Three, there is some additional discussion of octatoni• cism in the three pieces. 42. Perle, Serial Composition, 43. 43. Perle, Serial Composition, 41-42. Excerpts of the Sev• enth Sonata (pp. 42-43) illustrate such PC invariance in "sets" 123 (T-levels) a tritone apart. Jim Samson challenges some o-f these observations when he states: "In Serial Composition and Atonal- ity, George Perle has drawn attention to pivotal segments Dther than the 7/3 unit which create links between transpositions, no• tably the diminished seventh and the segment superimposing two minor thirds a perfect -fourth apart. Undoubtedly Skryabin made use of such pivotal segments as a means of linking and even (oc• casionally) combining transpositions, but I have found no evi• dence to support Perle's claim [excluded in the above quotation] that there is a "closed system of transpositions" based on these segments. The choice of transpositions in the seventh sonata has been governed by the tritone link and by the work's quasi- tonal structure, not mentioned by Perle." (Samson, Music in Transition, 209). In fact, in Trois Compositions, the frequent use of IC-3-related T-levels as the basis for harmonic succes• sions (often proceeding through three or more T-levels of a T- level cycle [e.g., "I", mm. 1-3, T-10,T-i,T-4,T-7,T-103), in combination with the interval 5 cycle, indicates a limited sys• tem of transposition. With regard to the term "pivot", another interpretation might include a single, "initiating" pitch which precedes other PCs of a given harmony. This occurs frequently with the harmonies of "I" and "III". Such a pitch would be piv• otal if it (or rather the PC) were common to the harmony preced• ing it as well as its own harmony. Of those adjacent harmonies with single, initiating pitches in "I", 71% have an initiating pitch which is pivotal (65% when one includes all adjacencies of harmonies), while 60% of adjacent harmonies with single, initi• ating pitches in "III" have an initiating pitch (56% including all adjacent harmonies. Hence, there is no strong tendency for such initiating pitches to act as pivots. 44. To reiterate and clarify, "element" represents the po• sition of a PC within an ordered collection of PCs—in this the• sis, a scale—with the element numbered according to the PC in• terval it forms with the first PC of the collection. The first PC of each PCC of the three pieces is determined by using the prime forms of the PCCs of "I" and "III", as they are most simi• lar when one excludes from consideration the variant PCs as shown in Perle's analysis. (Perle, Serial Composition, 43.) The prime form of the PCC of "I" has elements "0", "1", "3", "4", "6", "8", and "9" (Forte set 7-32), while that of "III" has ele• ments "0", "1", "3", "4", "6", and "8" (Forte set 6-Z24). (The numbering should not be confused with Forte's integer notation, where PC C is 0, Ctt/Db is 1, and so on.) While the prime form of the PCC of "II" differs from those of "I" and "III", there are certain similarities between the ICCs of the three pieces (as illustrated in Ex. 2-2). Hence, D, the first PC of the or• dered PCC at T-0 for "I", is element "0", Ctt/Db is element "0" in the PCC of "II" at T-0, and G is element "O" in the PCC of "III" at T-0. Again, the designation element "0" does not nec• essarily imply primacy of the PC represented by "0" in relation to the other PCs of the T-level. In fact, it may be rather dif• ficult for the listener to relate each PC to the "0" PC. How• ever, as will be noted in the discussion of "I", element "3" has 124 a limited form o-f primacy, given its -frequent occurrence as the initial element o-f many T-levels. 45. Gojowy, Neue sovtjetische Musik, 133. 46. Element successions in harmonic successions with the same T-level sequences were examined, whether the PC content and overall sequence o-f PCs was similar (i.e., a single ICC being used -for all three pieces) or not (i.e., individual ICCs used •for the pieces). Harmonic sequences whose T-levels were related by the same IC value (e.g., IC-3-related T-levels, such as T-O, T-3, T-l,T-4, and so on) and those that were not, thus all T- level successions, were investigated -for consistencies in ele• ment successions. Even element successions involving the same vertical positions (i.e., successions o-f elements in position one, two, three, and so on) o-f adjacent harmonies were evalu• ated. It appears that there are no consistencies indicative o-f principles o-f element ordering. Temporal ordering o-f elements not necessarily in the same melody or line, particularly ele• ments that are isolated or exposed (e.g., through single pitch attacks, or being outer elements o-f simultaneities) were exam• ined -for any patterns o-f ordering, revealing no consistent prin- c i p1es. 47. Similar references to PCs in this study will assume the use o-f PCs o-f the ICC at T-O (i.e., the ICC o-f the piece being examined, or o-f "I" i-f no reference to a piece is made). 48. In a discussion o+ chord structures in Roslavets'5 music, Gojowy indicates that the tritone is -frequently -found, while the perfect -fourth is infrequently used, and the minor second generally avoided. IC 1 usually appears as a major sev• enth or minor ninth. Gojowy provides one example from "I" (m. 6) where IC ls (in the form of minor ninths) are resolved to more consonant intervals. (Gojowy, Neue savjjetische Musik, 196- 197. ) 49. Although not discussed in Chapter Three, the tonal im• plications of vertical element occurrences are noteworthy. Ele• ments "O", "3", and "8" form the dominant chord of the minor to• nality suggested by the PCs of any of the three ICCs. (The PCs of the ICC of "II" actually suggest D minor and F major.) For example, elements "O", "3", and "8" (PCs D, F, and Bb) of the ICC of "I" at T-O form the dominant of Eb minor, the tonality suggested by the ICC PCs. In "II", elements "8" and "11", which frequently occur as uppermost pitches, are the mediant and domi• nant PCs of the major tonality that the ICC of "II" suggests. Elements "1" and "6" occurring frequently in the bass-lines are the tonic and subdominant PCs of the minor tonalities which the ICCs suggest. I 3-D CHAPTER THREE TONALITY IN TROIS COMPOSITIONS Introduction Roslavets suggests that classical tonality is completely absent in his works up to 1924, although "tonality as a concept o-f harmonic unity" exists in the form of the "synthetic chords."1 [Roslavets's system] was based on [synthetic] chords . . . used . . . as substitutes -for the -functional relationships o-f classical tonality, which he did not reject but rather tried to expand. . . . Composition based on the manipulation o-f tone complexes [i.e., the synthetic chords] may at times approach the tech• nique o-f twelve-tone writing. . . . This, however, occurs -fortuitously, not out o-f necessity. The meth• od may also generate other structures unrelated to twelve-tone procedures [i.e., tonal structures3.25 The significance o-f Roslavets's compositional technique is noted by Goj owy: This system o-f transposing tone-complexes is to be observed principally in the composers of the Mos• cow region. However, one need not regard this neces• sarily as as a revolutionary revival of composition: Roslavets regards his system not so much as the means of emancipation from tradition as an instrument for imposing order in opposition to the present impres• sion istic-ex pressionistic tonal anarchy, which guides music to a dead-end.9 Chapters Three and Four explore structures and procedures of other systems of PC organization in Trois Compositions. Of particular interest are tonal, actatonic, and dodecaphonic ser• ial ordering procedures. Initially, we will be concerned with tonali ty. 126 Although this present study centers primarily on more con• ventional tonal structures and procedures (i.e., characteristic o-f the "common practice period"), Roslavets* s ICC system may represent an expanded tonal system, in the sense o-f Wallace Berry's definition o-f tonality,** whereby these conventional ton• al structures and procedures are but one -facet o-f Roslavets's ICC system. The system has an apparent hierarchy o-f T-levels, with T-O as a referential harmony or "pitch-class-complex of resolution,"" as well as procedures for harmonic succession (i.e., the use of cycles of T-levels in ICs 3 and 5). The hier• archy Df T-levels as well as certain symmetrical characteristics of T-level successions and of IC-3-related T-level families sug• gest certain mi dd 1 eground/background structures'9 not unlike such large-scale structures in tonal compositions. It is from the resources of this expanded tonal system that Roslavets derives tonal structures and procedures. The nota- tional orthography for ICC PCs of "I" and "II" in particular, the fact that all three pieces have ICCs resembling the minor scale, and the fact that certain harmonic successions are based on IC-5-related T-level successions (which resemble tonic-sub- dominant or tonic-dominant progressions) indicate that the ICC system is contingent in part on traditional tonal procedures. This study will involve an examination of the individual pieces for surface and midd1eground/background tonal implications and tonally suggestive procedures. 127 Tonality in "I" Surface Tonal Features Perhaps the tonalities most clearly suggested in "I" are Eb, D, and G (generally minor mode). This is not surprising as the most -frequently occurring T-levels in " I • (T-O, T-11, and T-4) consist o-f PCs -forming these minor scales, respectively (Ex. 3-1). Example 3-1. ICC T-levels T-0, T-ll, and T-4 in "I". T-0 (Eb MINOR) T-ll (D MINOR) ^0 ° T Note that two o-f the less significant tonalities in "I", F major and Bb major (mm. 7-8), are related to D minor and G mi• nor, respectively. Of course, not all harmonies suggesting the Eb, D, and G tonalities are necessarily derived from these re• spective T-levels, nor do these T-levels as they appear in the music necessarily suggest the respective tonalities. A T-level PC collection can suggest a number of different harmonic struc• tures, and a number of different tonalities. However, it is in• teresting to note that the most significant PCs of "I" (deter• mined by evaluating both frequency of occurrence and total time- 128 spans of all occurrences o-f each PC) include tonic triad PCs o-f these three tonalities. Example 3-2 provides a comprehensive analysis illustrating surface harmonic and melodic structures associated with these three tonalities. Example 3-2. Surface structures and progressions of Eb, D, and G tonalities in "I". [11 [21 (31 (41 T-O T-4 T-4 T-ll HARMONIES (HARMONIC SUCCESSION) 129 Example 3-2 continued. Ml [51 (6) 17] [81 ii I—vii—I I--A6,bII Eb: vii--- 1 vii--——I vii—I Bb: I F: vii 1——- [10-111 [121 [131 (T-3) (T-6) (T-9) T-4 (T-9) T-O 1 l 1 >- a o }o • 0 • J\ )" r- * ["fTT •'ix I TP-^ -TWT \ ° »lft II A: I vii7 c: I V IV OR 9: IV V/IV I V IV V/IV I v a: ii7 V7 Eb: I I I I To some degree, the temporal-textural con-figuration of har• monies permits a tonal interpretation, as in mm. 10-13. Even those simultaneities with six and more PCs imitate tonal tertian structures by placing apparent chord "roots," thirds, fifths, 130 and sevenths in the lower register o-f the harmonies as well as in exposed upper voices. There-fore, they can be interpreted tonally, as Ex. 3-2 shows in mm. 1-8. Many o-f the PCs that are not part o-f these tonal tertian subsets can be perceived as ton al chord extensions (i.e., ninths, elevenths, thirteenths, or chromatic alterations thereof) although this also depends upon vertical configurations. In general, the tonal harmonic analy• sis in Ex. 3-2 is self-explanatory, with some exceptions. The succession from D minor to Eb that involves the entire ty of m. 6 is reiterated but reduced in the first half of m. 7 to a D minor-to-Eb major harmonic succession that precedes the vii-I succession in F. Measure 8 involves a modified vii-I sue cession in Bb. What is interesting about the final three harmo nies of mm. 6 and 7 and of m. 8 are the tritone sequences and their implications of the Eb, D, and G tonalities (Ex. 3-3). (Of course, not all pitches indicate these tonalities, as is suggested by the references to Eb in m. 6 and Bb in m. 8.) Example 3-3. Tritone sequences of mm. 6-8 and their tonal implications. (61 (71 (81 Eb: I F: I— Bb: I 131 The -final harmony o-f "I", T-O ICC in "II", serving a connective -function between the two pieces.) An examination o-f middleground/background linear (i.e., primary melody- and bass-1ine-derived) structures, and midd1eground/background harmonic structures, will -further illu• minate tonal implications in the piece, and in particular the interactions o-f these three tonalities as suggested by the T-O harmony o-f m. 13. M i dd 1 eground/Background Linear Structures o-f "I" Pitches comprising the outer voices of a texture are criti• cal for perception, especially since the harmonies, comprising six and more different PCs (often with no octave doublings), produce a relatively thick texture, and generally progress by step motion. While certain linear structures or aspects thereof in the three pieces have tonal implications, there are others that do not. These are, nonetheless, discussed in this Chapter because of their apparent significance. One important aspect of linear structures in "I" is that of initiating single-pitch exposure. Initiating single-pitch exposure. The sequence of initial, textura1ly-iso 1ated single primary melody pitches7 is illustra• ted in Ex. 3-4 with open noteheads on the first of two staves. 132 The second staff involves a reductive analysis o-f this sequence o-f initiating pitches viewed as a background structure. Given the -frequency o-f IC 3 relationships between adjacent initiating pitches, it is possible to perceive such adjacent pitches as dyads, with three or more successive pitches related by IC 3 as chords. An IC relationship between two adjacent pitches other than IC 3 represents a "break," so to speak, with the second of these two pitches forming a dyad with a pitch following it. Example 3-4. Initiating single pitches in "I". [11 (21 [31 [41 [51 T-0 T-3 T-10 T-1 T-4 T-7 T-10 T-4 T-ll T-9 T-2 T-5 1 .' : • X j ; >*:... i III \ - i i i i ; [61 (71 (81 (10,111 [121 [131 T-ll T-0 T-il T-2 T-7 T-3 T-6 T-9 T-0 133 In most cases the duration o-f an initiating pitch equals or represents a significant portion o-f the time-span o-f the harmony to which it belongs. Hence, these pitches have a surface agogic value in addition to metric accent as a result of coincidence with metrically stronger time-points. Duration is thus as im• portant a characteristic of these initiating pitches as is pre• cedence. Therefore, Eb4 (m. 5), although preceded by grace notes Fb3 and Bb3, is thus considered a part of this sequence of initiating pitches. Similarly, the trill pitches of m. 8 as well as those fol• lowing the initial pitches of mm. 6 and 7 are deemed part of the sequence of initiating pitches because of their durations, and because they represent a continuation of that sequence through a chromatic ascent from the initial trill pitches of mm. 6 and 7 (D4-E4). The trill pitch D4 (and not E4) is the primary initial pitch, given the initial harmonies suggested in these measures. This sequence of initiating pitches could be thought of as a "pitch axis", a series of prominent pitches around which other pitches gravitate.*3 In the reductive summary of Ex. 3-4, the sequence of prim• arily IC 3 dyads, formed by pairs of these initiating single pitches, is seen to form a structure indicative of a large-scale plan of PC control. This series of IC 3 dyads chromatically as• cends from D-F to F-Ab, with arpeggiations of diminished-seventh harmonies (i.e., mm. 1-3 and 7-13). However, there appears to be a bifurcation in this structure in mm. 4-5 when the progres• sion from E-(G) can be perceived to descend as well, through Eb 134 to D. This alternate path is represented in Ex. 3-4 with a dash-line beam in mm. 4-7. Linear structures in "I". Example 3-5 presents a more com• plete illustration o-f linear structures in "I". The sequence of pitches includes those extracted -from the primary melody, the bass line, and those uppermost harmonic pitches (indicated in Ex. 3-5 with "X"s) that occur higher than current melody pitches. Primary melody pitches having durations longer than an eighth value are denoted with open noteheads while shorter-val• ued pitches are designated with solid noteheads. Example 3-5. Linear structures in "I". (11 (21 (31 (41 (31 (BIFURCATION IN LINEAR STRUCTURE) A\ u t—, b* \-> e—o_ fa, Arfa «— —W 11 4v *'^> -01 v—&- 9— n " i—m— & \>T 1 -**f> j -J-—V-n—£e—|— „ O— v- ——fro-1i u 135 Example 3-5 continued. [6] 171 181 [10-111 •V- •jlo ' Vin? ha ^5— «#3toT I > ± =»— pbfl J "—P fcs*- ^ a—: t=r- -/- a—*p—1 [121 [131 V 4 -4 JH -^H ————• ( f 00 -/=r* - V* •l. - -• -. —f There is a middleground structure in mm. 1-6 involving both primary melody and bass-line pitches, with the PC 1ines—sugges• ted by successions o-f certain prominent pitches"* — descending by ICs 1 and 2 (i.e., F4-E4-Eb4-D4 in the primary melody, and Ab2- G2-F2-Fb3-Eb4-D4) . D4 in -fact remains as an important structur• al pitch in mm. 6-13. In mm. 5-13, a middleground progression o-f G5-G86-G84-G4, involving both primary melody and upper regis• ter pitches, is apparent. A similar structure involves bass pitches in mm. 6-13 (i.e., D4-G#3-A2-G#2-G2). Again, there is an apparent descending tendency in the PC line suggested by these pitches. 136 Melodic fragments. Additionally, there are certain melodic fragments characterized by similar successive IC sequences that suggest another dimension of underlying linear structure (Ex. 3-6) . Some o-f the pitches are notated an octave higher to show similarities in IC sequence (numbers above the pitches). All noteheads are beamed together to identify melodic fragments, labelled with lower case letters. Example 3-6. Melodic fragments of mm. 1-5 and 10-13 of "I" (11 (21 (21 [31 (41 (51 (101 (121 ••' "B" "o* *p' (TRANSPOSED) IC PATTERN ( ) 5—2—2—1—2—1—2 5—2—1—2 5-2~3"2-3 5-2-1-2 3E 11-21 (2-31 (4-51 (10-131 is-10] 3 There is an antecedent-consequent relationship between fragments m and nf and o and p in that consequent fragments n and p, transpositions of each other, cadence by step to final pitches of three quarter values in duration, while the antece• dent m and o fragments are characterized by larger intervals moving in disjunct motion. Hence, as there is a connective PC 137 (F#) between -fragments m and n, so too there is a connection be• tween -fragments o and p, a progression between the -final G o-f o and the initial G** o-f p. This progression involves pitch activ• ity in mm. 6-8 (Ex. 3-7) . . • . - Example 3-7. The PC progression G-G*»/Ab in mm. 6-8. (61 (71 (8) (91 (101 (M. 5-10) -4* *7— T i* T f— » *»*— 4 *» ; ft i • Both G and G**/Ab are prolonged, in a sense, in mm. 6-8, thus emphasizing the G-to-G8/Ab progression in mm. 5-10. Stud• ies o-f PC -frequency and duration have indicated the general sig• nificance o-f G and Gtt/Ab in "I". In addition, there are tonal implications of this G-Gtt/Ab succession -for Eb tonality, which is also prominent in these measures. In general, the -frequent occurrence o-f such melodic se• quences (IC 5 -followed by a series o-f ICs 1 and/or 2), indicate such sequences are significant in "I", perhaps motivic. Bass-I ins linear structures. There are midd1eground/back- ground indicators of both Eb and G tonalities in the bass-1ine pitches (Ex. 3-8). 138 Example 3-8. Bass-line structure o+ "I". 111 121 (3) [41 [31 [61 17) ± i—1 1—1 *—1 3! 4* 4-. V 3 tft-3-RBwrej«Kia-TPT>. >i > ' —' ^ 77«— (81 [101 till (121 [131 3 (b)Q tonality: (11 (31 14) (31 (61 (71 (81 (10,111 (121 (131 2 g: V7 1 V-—bVI—V bll 1 139 The reiterated A2-G*t/Ab2 (mm. 10-11), the Ab2-G2 succession (mm. 1-4), the prominence o-f D4 (mm. 6-7), and the -final G bass pitch (mm. 12-13) might indicate a tendency towards G tonality (Ex. 3-8b). In addition, the reiterated primary melody D4 in mm. 12-13 reinforces G. However, tritones in the background structure suggest Eb tonality in the final measures. Of course, Eb minor with Gb replaced by G is suggested by T-O PCs (m. 13), this harmony indicating both G and Eb tonalities. Midd1eground/background harmonic structures of "I" Besides structures indicative of Eb, G, and D tonalities, the most significant T-levels of the piece as to frequency of occurrence and total time-spans (i.e., T-0, T-ll, T-4, T-3, T-9, and T-7),10 and "balanced" occurrences of IC-3-related T-level families (i.e., 3-0, 3-1, 3-2, 3-1, and 3-0)11 would all be sig• nificant factors of midd1eground/background structure of "I" (Ex. 3-9). 140 Example 3-9. Midd1eground/background harmonic structure of "I" . [11 (21 [31 (41 (31 (61 T-0 T-3 T-10 T-10 T-4 T-ll T-3 T-ll T-0 Tonality in "II" Surface Tonal Features As in "I", references to tonality in "II" are fleeting, ob• scured by non-diatonic PCs and the absence of tertian struc• tures. However, of all inferable tonal centers, F appears to be the most significant. The ICC at T-0, although similar to the D minor scale, actually resembles the relative F scale more close• ly: element "1" (D, T-O) is a variant element, and because ele• ment "11" (C), the dominant degree of F, is included in the ICC 141 of "II" (Ex. 3-10). Indeed, the PC hierarchy o-f "II" (based on PC occurrence and total time-spans) is indicative b-f F as the most significant PCs are diatonic to F, with dominant, tonic, and subdominant PCs at the top of the hierarchy. Example 3-10. ICC of "II" and its resemblance to F. ICC of "II" n o ELEMENTS 0 13 4 6 8 9 11 F SCALE 331 In some situations a vertical harmony will resemble the tonic chord of the major tonality suggested by the harmony's T- level.ta T-0 is the most significant T-level in "II" as indica• ted by a hierarchization of T-levels (based on T-level occur• rence and total time-spans). Other significant T-levels (from greater to lesser) are T-5, T-3, T-IO, T-8, and T-7, with the other T-levels each occurring only once. The temporal-textural characteristic of T-0 (m. 13) is such that it suggests a I-V-I progression in F (Ex. 3-11)5 the Fs are doubled and reiterated. Although the third and fifth of the F chord (i.e., A5 and C6) are part of the T-0 simultaneity, the temporal and textural sep• aration of the simultaneity and its short duration make it pos• sible to perceive it as a V7 chord in F situated between the 142 doubled F and*its recurrence (implied I). In comparison, other T-0 harmonies do not have such a temporal-textural configuration that -facilitates the perception o-f F structures (Ex. 3-11). Example 3-11. T-0 harmonies in mm. 13, 1, and 10-12. (131 111 110-121 T-0 T-0 T-0 In some sense, the T-5 harmonies adjacent to those T-0 har• monies in mm. 10-12 suggest auxiliary harmonies since -five o-f the seven T-0 pitches proceed by step to those o-f T-5. Other tonal surface features are presented in Ex. 3-12. 143 Example 3-12. Sur-face tonal features in "II". til (21 (31 (41 (31 (61 T-0 T-3 T-10 T-3 T-10 T-3 T-6 T-2 T-5 HARMONIES Eb: I tbll)-—I- (bll)—-I Bb: viI7 I-V7-I 144 Example 3-12 continued. C71 [81 [91 (10-121 113] T-10 T-3 T-8 T-ll T-4 T-7 T-O T-5 T-O 5 r + § V9 , T<"L. ^fec > I b# /I r* ,1,= l TV -9—9 ft: 3 T Ab: vi7—(VJ—I-V7-I F: I-V7-I E: vii7 I-V7-I The same textural-temporal configuration 0+ T-O (m. 13) characterizes T-5 (m. 6), T-3 (m. 7), and T-ll (m. 8), with each harmony suggesting a tonal tertian chord and conceivable local tonality (i.e., Bb, Ab, and E, respectively). The doubled E pitches (E2,E3) and the reiterations of Gtt and B (mm. 8-9: T-ll, T-4,T-7) prolong the E chord and tonality. And with T-5 (m. 6) and T-ll (m. 8), immediately preceding chords rein-force the im• plied tonalities (Bb and E, respectively) because lower pitches o-f the preceding T-2 and T-8 harmonies suggest dominant-func• tioning tertian chords (Ex. 3-13). 145 Example 3-13. Harmonies o-f mm. 6-9 and their tonal implications. 161 171 (8) (91 T-2 T-S T-10 T-3 T-8 T-ll T-4 T-7 5 IK !> 9^1 lb/ / ft* 2 f i » * 3 ^ 3! VP * 1 •6- + Bb: vii7 —I--V7--I E: vii7 I--V7--I »b: wl7 (V)-I--V?--I Another harmonic succession (similar to that o-f mm. 8-9) involving invariant PCs o-f tonal implication occurs in mm. 3-5 (Ex. 3-14). Example 3-14. Eb in mm. 3-5. (31 (41 (SI T-10 T-3 T-10 T-3 T-6 T-9 a 3i 2 146 The emphasis on Eb is due in part to the reiteration of the T-10,T-3 succession.13 Eb-triad PCs occur in the outer voices o-f the T-10 harmonies, and the E2 pitches (T-3) suggest an upper leading-tone to Dtt/Eb (i.e., bll). Although most of the T-10 PCs are diatonic to Eb, the Eb-triad PCs, especially G and Bb (due in part to their vertical configuration), are partially ob• scured by these other PCs. Hence, it may be more accurate to describe the occurrences of Eb pitches in the bass line as Eb "roots" rather than specifically describing the chords as Eb tr i ads. Midd1eground/background linear structures of "II" Diminished-seventh structures in mm. 6-9. Certain middle- ground /background structures, linear and harmonic, imply tonali• ty, especially F. An important component of the linear struc• tures in "II" is the segment in mm. 6-9. Between F6 (m. 6) and F5 (m. 9), two alternating diminished-seventh chords are formed by primary melody pitches, while a third diminished-seventh chord is formed by bass-line pitches. In Ex. 3-15a, these pitches are highlighted by beams, while in Ex. 3-15b open note- heads comprise the diminished-seventh chord of which the melody pitch is a component, solid noteheads denoting components of the other diminished-seventh chords. For example, diminished-sev• enth chord C-D**/Eb-Ftt/Gb-A is prominent in T-2 (m. 6) and T-8 (m. 8), whose melodic pitches form C-D#/Eb-F*»/Gb-A. Likewise, diminished-seventh chord D-F-Gtt-B is prominent in T-10 (m. 7), and in T-4 and T-7 (mm. 8-9). Example 3-15c suggests the essen- 147 tial chord progression governing the primary melody pitches o-f mm• 6 — 9• Example 3-15. Arpeggiated diminished-seventh harmonies in the primary melody o-f mm. 6-9. (a)Primary melody and bass-line pitches: (61 171 181 191 b 0 -0—±7J -?— I? r [ Q T-2 T-5 T-10 T-3 T-8 T-ll T-4 T-7 These melodic chords imply a harmonized "expansion" o-f the initial F86-F6 melodic succession -first in this middleground harmonic progression, is in -fact a component o-f initial harmonies in mm. 6 The third d i m i n i shed-sevent h chord (C**/Db-E-G-A#/Bb) occurs in the bass line o-f mm. 6-8. Also, note the coincidence between IC-6-related T-levels in mm. 6-9 (e.g., T-2 and T-3, T-5 and T-ll, T-IO and T-4) and the diminished-seventh chords (Ex. 3-15). The midd leground/background resolutions o-f structural as well as surface tritones, some including the melody pitches o-f mm. 6-9, indicate the significance of certain tonalities, espe• cially F. An analysis of linear structures articulated by the primary melody and bass line (Ex. 3-16) incorporates these pre• vious observations with a study of midd1eground/background tonal structures. 149 Example 3-16. Midd1eground/background linear structures of "II". HI 12) 131 [4] [51 [61 17) [81 191 [10-12) 113) The prominence o-f PCs F and C, the structural tritone reso• lutions suggested by the local tonal regions Bb (m. 6) and E (mm. 8-9), and "exposed" pitches1*1 strongly imply F. The Eb "root" (mm. 3-5), as well as outer-voice occurrences o+ Eb (e.g., mm. 6, 7, 8), act as a preparation -for the E-F structural resolut ion. ISO Mi dd 1 eground/background harmonic structures o-f "II" Example 3-17 presents these structures. Example 3-17. Midd 1 eground/background harmonic structures o-f "II". til 121 13,41 151 [61 171 18) 19] [10-121 [13] T-: 0 5 10 3 2 5 10 38 11 47 -0 500 The interval 5 cycle o-f T-levels underlying the harmonic sequence o-f "II" would not itself suggest a m i dd 1 eground/background structure, were it not -for cycle -fragments taken out o-f sequence and repeated, as well as the coincidence o-f certain T-levels with -formally important t ime-points. 151 Tonality in "III" Surface Tonal Features Of the three pieces, "III" represents PC organization that is the least tonal, partially because of the infrequent use of clear tertian tonal harmonies and tonal harmonic progressions. Even the notation of PCs of the ICC of "III" Example 3-18. The ICC of "III". ICC of "Iir ELEMENTS 0 1 3 4 6 8 9 10 11 61/Ab MINOR SCALE Yet, despite the apparent tonal nature of the ICC, it is not clearly exploited as a "tonal" resource in "III".1"* Example 3-19 shows a few surface features that do suggest tonal proce• dures and structures. 152 Example 3-19. Surface tonal structures in "III' (31 (41 (5-61 171 (81 [91 (10-111 T-I T-5 T-8 T-ll T-2 T-6 T-9 T-2 HARMONIES E fa 1 3/ 1/ TONAL FEATURES OF HARMONIES 1± 77 1 ,*.JL ^A S C*a ____*J!li "si^ A: V---I g: v-i-iv—-V7--I D: i—v F: I--V7 Eb: I '.j. v7 1 Bb: v [121 [131 [14-151 T-5 T-O T-3 T-O T-4 T-7 T-O Db: I or Gb: V In mm. 3-7, there is a series o-f IC-5-related PCs with most o-f the component pitches approached (at times with inter-regis- tral connections) as tonics, by upper and lower semitonal 153 1 ead ing-tones suggestive o-f an augmented-sixth chord on the •flattened supertonic degree (Ex. 3-20). Long stems and beaming at the bottom o-f the system indicate these tonic pitches. To a limited extent, IC 3 and 4 dyads -formed between pitches o-f indi• vidual harmonies (isolated by brackets in Ex. 3-20, second sys• tem) suggest tonal chords in a "tonicizing V-I" sequence; these tonal implications are indicated. Example 3-20. IC-5-related PC successions in mm. 3-7 o-f "III 131 (41 (5-61 171 (81 Fl B 0 6 C L-fJ il II—*Lil 11- Jl 1 l 1 Only in such PC successions o-f mm. 5-7 are tonalities rep• resented with any clarity, either because o-f the PC successions or because PC configuration suggests tertian harmonies. 154 Midd leground/background linear structures o-f "III" Example 3-21 illustrates the linear structures o-f "III". Example 3-21. Mi dd 1 eground/background linear structures o-f "III". Ill , 121 131 [41 13-61 171 — — ff— 1 —J tf—— -J- r *" .4-— .4- [81 [91 [10-111 (121 [131 [14-151 (11 [31 [41 (5) [71 [81 [91 [101 [121 [141 — «! :——yL. I —— = — ^ : M There is a clear midd1eground/background linear structure involving a PC ascent1" o-f primary melody pitches, including the registrally highest pitches in mm. 1-4. It continues to Cx4 (m. 7) and could be perceived to continue to Eb5 (m. 12). While such continuities have no speci-f ic tonal implication,1" they do a-f-fect one's perception o-f melodic motion and in this sense establish a perceptible path through the piece. A PC that occurs -frequently in the primary melody in close proximity to pitches o-f this "ascending" structural line is F#/ Gb. Ftt/Gb may in fact represent a secondary tonal center. This pattern o-f occurrence is shown in Ex. 3-22, where the structural line, represented by beamed pitches, are separated -from occur• rences o-f Ftt/Gb. Interestingly, such exposed occurrences o-f F#/Gb do not occur a-fter m. 7, the apparent terminus o-f the "ascending" structural line. Example 3-22. Ftt/Gb and the linear structures o-f "III". tl] (2) 131 141 15-61 17) (8) 191 HO) (121 (141 h— 1/ »< c - - - -p -4 -J—Mu— j— it ^— fr y+ \-» fX* K = hi -in— ' Fi/5t: I «7 156 A possible explanation o-f this F#/Gb involves interpreting the -final T-O (mm. 14-15) as a dominant ( Bass-line linear structures are shown in isolation in Ex. 3-23. Example 3-23. Bass-line structure in "III". (11 (21 (31 (41 (5-61 [7] [8] (91 r—^ ski-) -*»— * *'£ *> *t Bb: I- Eb: V- (10-111 [12] [131 [14-15] 3! Bb: IV Cl/Db Eb: I In mm. 12-15, the bass line is centered around and cadences on C*»/Db. A middleground progression of Eb2 (mm. 10-11) to Db2 (mm. 12-15), preceded by an enharmonically spelled, arpeggiated Bb triad (suggestive of a V-I PC progression in Eb), links these two phrases. In mm. 1-7, however, the bass line is not as clearly defined as it is in mm. 8-15 (given the short duration 157 of many bass pitches), which complicates the derivation of a mi dd1eground/background structure. On the other hand, an essen• tial bass line could be perceived to begin with G#2 (m. 1), as shown in Ex. 3-23. As a result, it may be possible to perceive mm. 12-15 as a "summary" of the PC events in mm. 1-11 because of the modified transposition of mm. 1-2 in mm. 12-13. Hence, the midd1eground/background bass-line structure would be reducible to certain salient PCs (Ex. 3-23, last staff). Interestingly, the ascending PC line (Bb-Cx) essentially involves mm. 1-7, while the bass-line structure includes mm. 8- 15, with m. 7 as an inter-registral bridge between the two structural lines, involving a descending PC succession D (Cx4>, C (C3), and Bb (A#2). This indicates some formal distinction between mm. 1-7 and 8-15, highlighted by parametric changes such as reduced tempo and generally slower harmonic rhythm (especial• ly mm. 5-11), and the partial transposition of mm. 1-2's T-level succession in mm. 8-9. Midd1eground/background harmonic structures of "III". The harmonies forming the middleground/background harmon i c structures in "III" are shown in Ex. 3-24. 158 Example 3-24. Midd1eground/background harmonic structures o-f "III" . [11 (21 [4] 15,61 [81 [101 (121 T-O T-7 T-7 T-O T-5 T-8 T-2 T-2 T-5 h (21 (41 [121 [141 T-O T-7 T-7 T-O T-5 T-5 T-O 3 i i 3* — The underlying symmetrical structure based on cyclic suc• cessions o-f T-levels (indicated earlier in Chapter Two) -forms the main component o-f a midd leground/background structure, wh i 159 also includes cadential and other structurally important harmo• nies not part o-f the cycles.1 0 With -few exceptions however, none 0+ these significant harmonies takes on explicitly tonal qualities, either in vertical configuration or in harmonic suc• cession. As with the linear structures discussed above, there is only a sense of proceeding to a following tonality in a fluc• tuant context, whether suggested by a single PC or by a tertian harmony, with no apparent return to or emphasis of certain har• monies, except for T-0 and, to a lesser extent, for T-5, T-8, T-2, T-7, and so on. In addition, there is no recurrent PC col• lection coincident with the recurring Ftt/Gb in mm. 1-7. As has been established in the previous analyses of the three pieces, "III" differs from the other two pieces in its surface and midd1eground/background harmonic and melodic charac• teristics. "Ill" seems to represent the more mature, or experi• mental, of the three pieces, involving fewer obvious references to tonal harmonic structures and procedures while using more linear structures in a more contrapuntal texture. Cone 1 us ion The three pieces exhibit some important features of conven• tional tonality. From the ICCs which are the basis of each piece, tonal structures and procedures are derived and employed in the pieces, especially in "I" and "II". In fact, some char• acteristics of the ICC system (e.g., the PC content of the ICCs) are evidently tonal, indicating that the system is contingent upon tonal procedures. However, tonal manifestation takes dif- 160 ferent -forms, and is dependent upon certain -features in the mu• sic to highlight the tonal aspects. For one thing, given the six to eight (and more) different PCs per harmony, and the many non-diatonic PCs, it is often difficult to perceive tonal ter• tian chords unless vertical and registral distribution of PCs highlights PCs of such chords. In addition, linear structures (both surface melodic features and midd1eground/background structures) need to adhere to certain tonal conventions (e.g., dissonance resolution, pitch successions such as ascending interval 5 cycles) and emphasize tonic and dominant PCs of given tonalities through PC reiteration and agogic accentuation. In "I", Eb, G, and D tonalities are most obvious and sig• nificant, suggested to some degree by clear tertian chord struc• tures of these tonalities, by surface melodic features, and also by midd1eground/background linear structures. In "II", surface features do not as clearly imply the piece's principal tonality, F, with the exception of the final harmony. Likewise, other subordinate tonalities are implied by transpositions of the fi• nal harmony. The linear structures, both surface and middle- ground/background, are responsible for conveying the impression of F. In "III", tonality is at best fluctuant. There are tem• porary indications of certain tonalities (e.g., A, D, and G, as• sociated with the interval 5 PC succession, mm. 5-7; C#/Db, mm. 12-15) but no recurring, clear indications of any tonality. Un• like the T-0 harmonies of "I" and "II" that are not only refer• ential sonorities in the sense of being hierarchically important but also incorporate tonic triads of the respective tonalities, 161 the T-O harmony of "III" does not readily suggest a tonic triad •for any tonality.1" Certainly, tonal structures and procedures cannot be ad• duced to explain all PC occurrences and -functions. An inferred tonal system does, however, allow one to perceive musical motion and relationships between musical events with respect to ves• tiges of -familiar tonal procedures and structures. Notes 1. Roslavets, "Roslavets"-^, 397. 2. Gojowy, "Hal-f Time," 212. Elsewhere, Gojowy indicates the non-functional nature of harmonies in Roslavets's music, despite their correspondence to romantic chord structures. (Gojowy, Neue sowjetische Musik, 196.) 3. Gojowy, Neue sovijetische Musik, 146; my translation. 4. Berry states: "Tonality may be thus broadly conceived as a formal system in which pitch content is perceived as func• tionally related to a specific pitch-class or pitch-class- complex of resolution, often preestab1ished and preconditioned, as a basis for structure at some understood level of perception. The tonal system consists of a hierarchic ordering of PC fac• tors, with the tonic (final, axis, center, etc.) the ultimate point of relationship which tonal successions are contrived to "expect." ... In more recent styles in which tonality is rele• vant a system may (but need not) consist of specific scalar for• mulations (PC collections) of these or other kinds, with deriva• tive melodic and harmonic configurations disposed in such a way as to express and give primacy to a particular "tonic" or, in fluctuant contexts, particular "tonics." Often such tonal con• tent is reminiscent of conventions of the tonal period. (Berry, Structural Functions, 27-28.) 5. Ibid. 162 6. In this thesis, "middIeground/background" indicates some underlying or non-foreground aspect or structure. Although the combination o-f the two Schenkerian terms may be con-fusing and contradictory, and although the pieces are not tonal (hence, a rather loose application o-f the two Schenkerian concepts to the pieces), their use together is apt, considering that there is oftentimes more than one non-foreground level. Moreover, it is difficult to differentiate the "middleground" from the "back• ground" in this music; hence, the more general designation "midd1eground/background" to indicate any or all non-foreground structures or aspects, rather than one term or the other. 7. Exceptions to this use of an initiating single-pitch exposure are: T-0, T-1, and T-0 harmonies (tin. 6), T-2, T-3, and T-2 (m. 7), and T-7, T-8, and T-7 (m. 8). Significantly, these measures are a distinct formal unit. 8. This is similar to the idea of pitch axis as expounded by Richard Chrisman in his Ph.D. dissertation "A Theory of Axis- Tonality for Twentieth-Century Music" (Ph.D. dissertation, Yale University, 1969), 22f. To quote Chrisman, a pitch axis is "a line or series of points about which other pitch structures are arranged." This term is, according to Chrisman, relatively -free of associations with tonic-dominant tonality and free of specif• ic functional associations (p. 22). Some of Chrisman's analyti• cal processes (e.g., determining significant PCs and T-levels through calculation of occurrences and total time-spans through a given piece) are employed in this thesis. 9. A PC line is a series of successive PCs, in this case representing actual pitches in the music, although the pitches are not located within one register or octave, and need not be adjacent to each other. In "I", the PC lines have a descending tendency (e.g., the PC line Ab-G-F-Fb-Eb-D, mm. 1-6, represent• ing bass pitches). A "prominent pitch" is one that is usually temporally and/or registrally isolated (e.g., in the outer voices of the texture), often having metrical and/or agogic ac• centuation. In "I", the single initiating pitches are examples of prominent pitches. 10. The hierarchy of T-levels, in descending hierarchic or• der, is: 0, 11, 4, 3/9, 7, 2, 5, 6/10, 1. T-8 is not used in " I " . 11. The 3-0 family of T-levels includes T-O, T-3, T-6, and T-9; 3-1 includes T-1, T-4, T-7, and T-10; and 3-2 includes T-2, T-5, T-8, and T-ll. 163 12. As stated earlier, two tonal tertian chord components as the lowest pitches and another component as the highest pitch would -facilitate tonal interpretations o-f more complex harmon• ies. Such harmonies are: T-10, mm. 3-4 (Eb); T-5, m. 6 (Bb); T-3, m. 7 (Ab)5 T-ll, m. 8 (E); and T-0, m. 13 (F). 13. The PC content o-f T-10 corresponds to the Eb-major scale. This also suggests the reason why T-10 and T-3 were re• moved -from the interval 5 cycle that is the basis o-f T-level successions in "II". 14. To reiterate, "exposed" pitches refer to those that occur in outer voices of a homophonic texture, or that are rhythmically or temporally isolated in some manner. For ex• ample, A#/Bb in mm. 1, 4, 5, 8, and 10-12; and E in mm. 3, 4, and 5. 15. Interestingly, the PC content of the ICC of "III" does suggest a potential approach to understanding PC organization. This involves subdividing the ICC into subsets, based on the accidentals of the PCs as notated. In other words, G, Bb, and Db (elements "O", "3", and "6", respectively) form one subset while Gtt, B, and D# (elements "1", "4", and "8", respectively) form another. In fact, the G-Bb-Db subset forms a vii-i rela• tionship to the Gtt-B-Dtt subset, when one of the two is enharmon- ically understood. There are some instances where two- and three-pitch subdivisions of harmonies, produced by temporal- textural configurations of pitches (such as dyads formed by sim• ultaneously attacked pitches), involve PCs of one subset or ano• ther. This principle of PC location is however not consistently applied to all harmonies, nor is the above-mentioned "vii-i" relationship exploited in the temporal-textural configurations of individual harmonies. 16. Ascending PC line refers to a non-literal ascent in the sense that there is no constant ascent within one register. In "III", the PC ascent is: Bb5-B5-C5/C6-C#4-Cx4. 17. Each two-pitch succession suggests a 1eading-tone-to- tonic succession. 18. To reiterate, this structure includes the T-7-centered cycle (3-1, mm. 2-4), T-O (m. 4), and the T-5-centered cycle (3-2, mm. 4-13), with an initial T-0,T-5 succession (m. 1) and final T-7,T-0 succession (mm. 13-15). Both T-5 and T-7, IC-5-related to T-0, have a somewhat symmetrical or "opposing" relationship. These T-levels T-O, T-5, and T-7 have associa• tions with tonality at least on a superficial basis (i.e., T-O being "tonic", T-5 being "subdominant", and T-7 being "domin• ant"). The hierarchy of T-levels in "III", based on frequency of occurrence and total time-span, is! T-O, T-5, T-8, T-2, T-7, T-ll, T-4, T-9, T-1, T-6, T-3, and T-10. Hence, the more sig• nificant T-levels of this hierarchy would be included in the middleground/background harmonic structure. 164 19. As suggested by Ex. 3-22, it could be, on the other hand, the dominant o-f Ftt/Gb. I OTHER SYSTEMS OF PITCH-CLASS ORGANIZATION IN TROIS COMPOSITIONS Our attention is now turned to systems of PC organization that are to some degree apparent in the three pieces, namely octatonicism, and serialism. Octatonicism, which will be considered first, can be clas sified as a form of tonality in the general sense of the term because of its hierarchization of PCs. Because Russian contem poraries of Roslavets (e.g., Nikolai Rimsky-Korsakov, Stravin• sky, and Scriabin) used the octatonic collection as a basis fo some of their music,1 we need to investigate the extent of its applicability in Trot's Compositions. Example 4-1 illustrates the resemblance of the ICCs of the three pieces to octatonic col 1ecti ons. 166 Example 4-1. ICCs o-f Trois Compositions compared with octatonic collections. ICC OF "I" AT T-O ICC OF -ir AT T-O m OCTATONIC (1 - 2! D) OCTATONIC (1 - 2; CI) 3*= Jo "bo h OCTATONIC 12 - 1! 0) OCTATONIC 12-11 CI) 0 _ 0 cr o — V OCTATONIC (2 - If Ob) OCTATONIC (2 - ii CI h *> IT ICC OF 'III' AT T-O ltd OCTATONIC (1 - 25 6) OCTATONIC 12 • 1} 61 OCTATONIC (2 - li 6bI HE The ICC o-f "I" closely resembles octatonic collection 1 (i.e., semitone-tone) while that o-f "II" resembles both octa tonic collections 1-2 and 2-1, with each ICC having six o-f eight PCs common to those o-f the respective octatonic collec 167 tion. With the ICC of "III", there are five PCs matching the octatonic collection 1-2. Deliberate use of the octatonic collection might be indi• cated by some consistency in the temporal-textural location and/or function of ICC elements not belonging to the closest octatonic collection. Although non-octatonic elements usually occur in functionally less significant situations,2 such pat• terns of occurrence are still not consistent enough to be strongly indicative of deliberate octatonicism. The fact that these non-octatonic elements are components, albeit inner- voice components, of the various harmonies would seem to rule out the idea that Roslavets used the system at all. All ele• ments appear in nearly all vertical positions of harmonies. Invariant and "quasi-invariant" PCs in T-level families of "I" and "III" Taruskin's descriptions of octatonicism in the latter's music (see Chapter Two, fn. 40), there is no readily apparent pat• tern of location or function of non-octatonic PCs of a T-level family. Hence, the octatonic system does not appear signifi• cantly applicable to PC events assessed as to function and pos i t i on.3 168 Serial PC Organization In the pertinent literature, there seems to be some con• flict regarding the extent to which Roslavets's music reflects dodecaphonic thinking. Some writings refer to the composer as a "Russian Schoenberg."** In fact Gojowy's earlier writings indicate that he may have regarded aspects of Roslavets's works to be dodecaphonic. These are, for example: a reference in Gojowy's Neue sowjet ische Musik to Roslavets's use in "II" of "all twelve levels of one complex . . . in a perceivable methodical ordering;""* an earlier reference in this same text to "the prompt reappearance of a transposition- level" being "usually avoided—a principle that likewise underlies the twelve-tone row;"** and an earlier article by Gojowy entitled "Nikolaj Andreevic Roslavec, ein fruher Zwo 1 f tonkompon i ert. '"* Perle qualifies his use of the terms "set" and "series" with regard to the music of Scriabin and Roslavets. Initially he defines the term "set" as comprising "all 12 notes of the semitonal scale, arranged in a specific linear order" and that "Cno3 note appears more than once within the set."° Later, he states: In a strict sense the term "series" denotes an or• dered succession of elements, such as the Schoenbergian 12-tone set. Hauer*s "tropes" are only partially ordered, while in the works of Scriabin and some other composers the set is a collection of pitches the specific ordering of which is purely compositional. The term "serial composition" is used in the present study as a general designation for music based on any of these types of sets.** 169 In addition, Perle states: "[The] term unordered set will designate such a collection . . . employed . . . only in a single aspect [i.e., not applicable in inverted and retrograde forms], as in the works of Scriabin; for ... a specified succession of the notes [is not] assumed to be a defining characteristic of the set."lo Recently, Gojowy has suggested that Roslavets's music was not intentionally dodecaphonic. Through systematic application of such transposi• tions [i.e., through the use of all twelve T-levels], Roslavets's compositions revealed elements similar to dodecaphonic serial thinking as early as 1914-15 in the works mentioned above. For this reason, George Perle LSerial Composition and Atonality, pp. 40-44] has classified Roslavets's system, together with that of Scriabin, as "nondodecaphonic serial composition." I cannot entirely agree with this designation, since it seems to imply that the Russian system amounted merely to a kind of pre-figuring of the fully dev• eloped twelve-tone system. In reality, the Russian system, which had already been identified as such in Scriabin's work by the Polish musicologist Zofia Lissa in the 1930's, stands as an independent method with its own principles. A series or row, whether dodecaphonic or not, is defined by the invariable order of its members. But in the tone complex, as used by Scriabin and Roslavets, the order of its elements remains free; the complex is defined only by its intervallic structure. Composition based on the manipulation of tone complexes may at times approach the technique of twelve-tone writing, as happens occasionally in Roslavets as a consequence of his particular choices of scale degree for transposition of a tone complex. This, however, occurs fortuitously, not out of necessity. The method may also generate other structures unrelated to twelve-tone proce• dures . 1 *• While there is no apparent use of invariant PC ordering characteristic of serial music as previously established in 170 studies of element ordering, there are aspects o-f Roslavets's music that approach serial dodecaphonic organization. Such organization is not consistently applied, thus reflecting no conscious use o-f serial techniques. Yet, its existence is nonetheless important, symptomatic perhaps of the highly chro• matic and sometimes atonal musical styles prevalent in the post-Romantic era at the time of Trois Compositions. An examination of T-level successions and certain melodic segments of the three pieces will illustrate such serial and/or dodecaphonic sequences.12 Serial Ordering of T-Levels and of PCs in T-Levels The succession of T-levels in the three pieces is "quasi- serial" in the sense that all or most T-levels are used in the three pieces individually while certain T-levels are reitera• ted. Moreover, there appears to be some coincidence between the completion of the series of twelve T-levels and formally important time-points. This is shown in Fig. 4-1, with the first occurrence of each T-level given separately below the sequence of T-levels. Figure 4-1. Serial ordering of T-levels in Trois Compositions. •I" MEASURE: 1 2 3 4 3 6 7 8 10,11 12 13 T-LEVEL: 0-3-10 1-4 7-10-4 11-9-2 5 11-0 11-2 7 3-6 9-4-9 0 T-LEVEL*S FIRST (T-8 OCCURRENCE: 0-3-t0--l-4--7 tl-9-2-3- 6 lissing) 171 Figure 4-1 continued. •II" MEASURE: 1 2 3 4 5 6 7 8 9 10,11 12-13 T-LEVEL: 0-5 8-1 10-3 10-3 6-9 2-5 10-3 8-11-4 7 0-5 0 T-LEVEL*S FIRST OCCURRENCE: 0-5--8-1-10-3 6-9-2 11-4--7 •nr MEASURE: 1 2 3 4 3,6 7 8 9 10,11 12 13 14 T-LEVEL: 0-5 8-3-7-10 1-4 7-0-5 8 11 2-6 9 2 5-0 5-0-4-7 0 T-LEVEL'S FIRST OCCURRENCE: 0-5--8-3-7-10--1 -4 11 -2-6-9 In "I", the series-final13 T-level (T-6, m. 10) occurs in the first measure of the recapitulation. In "II", the series- final T-level (T-7, m. 9) precedes the recapitulation in m. 10. In "III", the series-final T-9 (m. 9) forms with T-2 (mm. lO-ll) the cadence which precedes the recapitulation in m. 12. Despite the six to eight different PCs per harmony, there is no true PC complementarity involving PCs of adjacent harmon• ies. At least one and usually more PCs are not part of two ad• jacent harmonies, with completion of a PC series involving three or more adjacent harmonies. Moreover, there is no consistency in occurrences and completions of such PC series, in terms of registral or temporal location. 172 Serial Ordering o-f Melodic Pitches Certain primary melody and bass-line segments of the three pieces exhibit limited -forms o-f serial ordering. Again, what is o-f interest is the coincidence o-f series-final PCs with -formally important time-points. Additionally, many PCs o-f individual se• ries are stated in initial measures o-f the respective pieces, a sign o-f the chromatic nature o-f these melodies. Example 4-2 presents the primary melodies and bass lines o-f the pieces, and indicates the PC series involved with each. Melodic pitches are designated both by staff notation and by PC numbers. T-levels are also indicated for the purposes of comparison. Example 4-2. Serial ordering of primary melody and bass-line PCs. •r N.: (11 (21 (31 141 (51 T-: 0 3 10 1 4 7 10 4 II 9 2 5 " 1 : i i r—to » ' "°— * • ..... „ l» ' - 1 5 10 0 2 1 3 4 6 11 9 1 1 1 ! 1 1 1 • i bo f ~n—^ » t I r* rT> 8 9 6 031275410 (11 NISSIN6) «.: [6] (71 [81 (101 T-: 11 0 11 2 7 3 6 (T-8 NISSIN6) (8) 8 173 Example 4-2 continued. •II* M. (11 [21 131 (41 151 161 171 [81 T- 0 3 8 1 10 3 10 3 6 9 2 3 10 3 8 11 (T-4,7 IN M. 8-9) H —r 0 2 3 6 7 8 10 1 11 (4 NISSIN6). *> 'ft Ibo 1 BSE 10 9 6 3 3 4 0 8 1 (11 NISSIN6) •nr N. (11 (21 (31 (41 T- 0 3 8 3 7 10 1 1 4 7 0 5 to far• ^ V 1° I I az i_ !E 3* x 10 4568932 11 7 1 jfa± •*c— TT ZZ = 8 4 11 10 2 9 N. 13-61 (7) (81 (91 (10-11) (12) T- 8 11 2 6 9 N— 0 6 7 3 1 174 The primary melodies o-f "I" and "III" and the bass line o-f "III" have twelve PCs each. The primary melody and bass line o-f "II" and the bass line o-f "I" have eleven PCs each. In addition, there is a certain amount o-f coincidence be• tween the series-final PCs and formally significant time-points, at least in "I" and "II". The series-final bass-line PC in "I" T-level (T-6) coincide with the recapitulation. (There is how• ever, an earlier significant occurrence of G# CG#6, m. 73, the pitch climax in the piece.) In "II", both the series-final pri• mary melody PC (A) and the series-final bass-line PC (Db) occur in m. 8, adjacent to m. 9 and the series-final T-level (T-7), which precedes the recapitulation. In "I" and "II", there is a relative coincidence of series-final PCs and T-levels with each other, and with formally important time-points. Such coinci• dence is not as evident in "III", however, with disjunction of the series-final primary melody PC (C#, mm. 5-6), the series- final bass-line PC (Ctt, m. 12, coinciding with the recapitula• tion), and the series-final T-level (T-9, m. 9). The latter does, however, form a cadence with the T-2 harmony (mm. 10-11) preceding the recapitulation. In all three pieces, there are no apparent repetitions of numerical sequences representing the se• ries of PCs or T-levels, or of IC patterns underlying such PC and T-level series (although there are limited similarities un• der inversion in the IC pattern underlying the T-level series). 175 It is difficult td determine whether completions of such partially or fully dodecaphonic series are coincidental or are deliberate. The recurrences of T-levels, T-level successions, and melodic-harmonic figurations in "I" (mm. 10-13) and "II" (mm. 10-13), and the reiteration of such material within these recapitulative measures, indicate a complete use of all original pitch and rhythmic material by m. 9 of both pieces. In one sense then, there should be some manner of coincidence between this formally important time-point, the recapitulation, and com• pletion of PC or T-level series. Whether these series represent deliberate dodecaphonic serial ism is questionable since some of the series (particularly those involving T-levels) are based on non-dodecaphonic, non-serial techniques (e.g., the interval 5 cycle of T-levels which includes all twelve T-levels). However, such series, whether deliberate or not, are manifestations of the highly chromatic nature of Roslavets's music. Notes 1. Some writings that examine octatonicism in early 20th- century Russian music are: Arthur Berger, "Problems of Pitch Organization in Stravinsky," Perspectives on Schoenberg ana" Stravinsky, ed. Benjamin Boretz and Edward T. Cone (New York: W. W. Norton, 1972), 123-154; Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983); and more recently, Richard Taruskin, "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'," Journal of the American MusicologicaI Society, 38/1 (Spring 1985): 72-142. 2. In general, non-octatonic elements occur in less signif• icant situations more than 50% of the time. In "I" the non-oc- tatonic element is "8"; in "II", "1" (the variant element) and "4"; and in "III", "8" and "11" (one of the three variant ele• ments). In the case of element "8" in "I", 17 of 25 occurrences of the element can be described as functionally less signifi• cant, that is, in a relatively concealed inner voice, or on a 176 relatively weaker metric time-point, sometimes with a corre• spondingly short duration. (6 of these 17 occurrences are in the primary melody, on weaker metric time-points and with short durations.) O-f the 24 individual harmonies or T-levels in "II", the non-octatonic element "1" occurs only three times (in the bass line) while element "4" occurs -fourteen times in more ex• posed outer voices although only eleven o-f these can be de• scribed as -functionally significant situations according to the criteria stated above. On the other hand, i-f one were to con• sider the octatonic 1-2 scale as the referential collection, then elements "8" and "11" would be non-octatonic. Element "8" occurs 75% of the time (i.e., in 75% of element "8"'s occur• rences) as an inner-voice pitch although it occurs in half of the T-levels as the second highest pitch in the harmonies (and seven times in the outer voices). Element "11" occurs 60% of the time as an inner voice pitch although it occurs 40% of the time as the second highest pitch in the harmonies (and ten times in the outer voices). In "III", element "8" occurs 66% of the time as a less significant outer-voice pitch or an inner-voice pitch, while element "11" occurs only twice in the piece, each of these as a less significant melodic pitch. 3. To reiterate, certain observations made by Taruskin con• cerning octatonicism in Scriabin's later music (Taruskin, "Stravinsky's 'Angle'," 99, fn. 47) have implications for Roslavets's music: the three octatonic sets (or IC-3-related T- level families) act as referential collections, functionally akin to keys in the traditional sense; a sense of tonal motion achieved by modulations from one octatonic grouping to another, or, in the case of the three pieces, transference from one T- level family to another; and the return to the same octatonic key (T-level) with which the piece began. There may be some basis for the application of octatonic theory and structures to the music of Roslavets, if not to the three pieces in particu• lar. However, one point of difference between the music of the two composers is the fact that, in Scriabin's later music, the octatonic collection "does not interact with diatonic harmony or emphasize triadic cognates" (Taruskin, "Stravinsky's 'Angle,'" 99, fn. 47), while diatonic harmonies and triadic cognates are observed to exist, albeit in a limited way, in the three pieces. 4. One such reference occurs in Schwarz, Music and Musical Life in Soviet Russia, 86. 5. Gojowy, Neue sowjetiscAe Musik, 171-2, in a section entitled "Fruhe Ansatze von Zwd1ftontechnik bei Roslavec und Lourie: Zwolftontechnik und Zwo1ftonkomp1exe." 6. Ibid., 140. 7. Gojowy, "Nikolaj Andreevic Roslavec, ein friiher ZwoIftonkomponist," Die Musikforschungt 22/1 (January-March 1969): 22-38. 177 8. Perle, Serial Composition, 2. 9. Ibid., p. 40, fn. 1, in a chapter entitled "Nondodeca- phonic Serial Composition." 10. Ibid., 46. 11. Gojowy, "Hal* Time," 212. 12. Some o-f Gojowy's analyses o-f Roslavets's works likewise deal specifically with identification of dodecaphonic and non- dodecaphonic series. 13. "Series-final" means the final PC or T-level of a ser i es. 176 CHAPTER FIVE CONCLUSION The ICC System What can we conclude about Roslavets's compositional tech• niques in Trois Compositions'? Each piece has a complex PC orga• nization, involving a basic ICC realized as a PCC at various T- levels, whose content can be varied within certain limitations. Transposition and element variance o-f a referential PCC thus de• termine the content o-f most PC collections in a given piece, ex• pressed vertically, divided into sparser harmonies made up of ICC subsets, and, in a few instances, linearized. The ICCs of the three pieces differ in PC and element content. One T-level (T-O) acts as a referential sonority -for the given piece, in the sense that the sonority begins and concludes the piece, and is most significant as to frequency of occur• rence, greater total time-span, and coincidence with formally important time-points. All T-levels can in fact be hierar- chized, as to these criteria, in assessment of the significance of each in a given piece. T-5, T-3, and T-8, aside from T-O, are significant T-levels in the three pieces. Successions o-f T-levels are generally based on ascending interval 3 and 5 cycles. Particularly in "I" and "III", three or four T-levels of an interval 3 cycle are employed in an as• cending succession, before yielding to another interval 3 cycle 179 or component (s) thereof. PC invariance in al'l four (or even three or two) T-levels o-f a -family o-f IC-3-related T-levels, and transferences from one family (or component) to another, are somewhat analogous to the PC collections of tonal keys and modu• lations between such keys. In fact, many of the transferences from one interval 3 T-level family (or component) to another in• volve IC-5-related T-levels. Since the three different interval 3 T-level cycles can be mapped onto the interval 5 cycle, as shown in Chapter Two, it is possible to view the interval 3 T- level families as components of the interval 5 cycle. There are no readily apparent consistencies of PC and ele• ment occurrence and ordering, within individual PC collections or through adjacent collections, indicative of deliberate con• trol. Because most T-level successions involve IC-3- or 5- related T-levels, there are on average three or four invariant PCs in a given succession, one of these involving pitch continu• ity. Likewise, there are no apparent, consistently applied principles of voice leading or pitch succession, despite Roslavets's indication to the contrary, although these may have evolved with later works. There are, however, certain limited tendencies in element occurrence (i.e., in the primary melodies and bass lines of the three pieces, and in ranges of vertical positions) and ordering (i.e., similarities in vertical element orderings of harmonies, as well as frequent occurrences of certain element adjacencies), tendencies suggesting that elements, and not just PCs, are de• terminants of chord structures. 180 Tonality, Octatonicism, and Serial ism The ICC system and various principles discussed above con• stitute an "expanded" tonal system, which can be manipulated to produce different types of structures, including tonal struc• tures. In a sense, two systems are employed at once: a theor• etical ICC system, and a more perceptible tonal system. The ICCs resemble tonal scales, and have consequent potential for tonal exploitation. In "I", three tonalities--D minor, Eb (major/minor), and G minor — are evident, while one tonality, F, is evident in "II". Tonality in "III" is best described as fluctuant, involving references to various tonalities, since it is difficult to identify any pervasive centricity. Studies of midd1eground-background structures in fact reveal large-scale tonal structures and procedures in "I" and "II", which are not readily apparent in "III". Moreover, while tonal exploitation of harmonic resources of a given piece is dependent upon, and may be limited by, prior decisions concerning the ICC system and T-level successions, there are instances where ICC system-based structures and successions are altered to allow for tonal impli• cations (one example being the repetition of T-10,T-3 C " 11", mm. 3-43, for emphasis on Eb triad components of T-10). Both octatonicism, which can be a basis of tonality in the broad sense of the term, and serial ism (both dodecaphonic and non-dodecaphonic) are applicable to a limited extent in Trois Compositions. Such inconsistent use of octatonic and serial methods, quite uniike the deliberate use of tonal structures and 181 procedures in the pieces, is typical o-f the music o-f the com• poser's era. Implications o-f "III" Concerning Matters o-f Style and Large-Scale Form As little is known about details o-f Roslavets's li-fe, his compositional activities and practices, influences upon this music, and his personal and professional contacts, there is much upon which one can speculate. One matter, arising in the pre• sent study, upon which one can make some interesting and impor• tant speculations, is the circumstance of pronounced differences between "I" and "II" on the one hand, and "III" on the other. Plausible reasons for such differences could be: a time lapse between the composition of the first two pieces and the third, intervening influences from various sources, and/or deliberate redirections in Roslavets's compositional techniques. Whatever the actual reasons for these differences, "III" would seem to represent the more experimental and, perhaps, mature of the three pieces, one involving fewer references to tonal proce• dures, more linear structures, and a more contrapuntal texture. On the other hand, there are certain similarities between "I" and "III" that perhaps suggest their formal association, even suggesting a large-scale ternary form in Trois Compositions as a whole. This study has established some basic principles of Roslavets's compositional technique, based on Trois Composi• tions, which belong to an early phase of the composer's career. 182 It is hoped that it will contribute to a deepened understanding and appreciation o-f Roslavets's music, which is largely unknown, and will encourage -further study and performance o-f this music. With such study, the composer and his music will be accorded a position of deserved importance in twentieth-century Russian musical development. IS2> SELECTED BIBLIOGRAPHY Abraham, Gerald. "The Reaction Against Romanticism: 1890- 1914." In New Oxford History of Music, edited by Martin Cooper, vol. IO, 80-144. Toronto: Ox-ford University Press 1970. Asa+iev, Boris. Russian Music from the Beginning of the Nine• teenth Century. Translated by Al-fred J. Swan. Ann Arbor, Michigan: J. W. Edwards, 1953. Berry, Wallace. Structural Functions in Music. Englewood Cliffs, New Jersey: Prentice-Hall, 1976. Chrisman, Richard. "A Theory o-f Axis-Tonality for Twentieth- Century Music." Ph.D. diss., Yale University, 1969. Das Srosse LexiMon der Musik. 1982 German ed. of Diet ionnai re de la Musique. S.v. "Ross 1awetz," by E. Stockl. Die Musik in Geschichte und Segenwart. S.v. "Roslawetz, Nikolai Andrejewitsch," by Guido Waldmann. Forte, Allen. The Structure of Atonal Music. New Haven, Con• necticut: Yale University Press, 1973. Gojowy, Detle-f. "Nikolaj Andreevic Rosl avec, ein -fruher Zw61f- tonkomponist." Die Musikforschung. 22/1 (January-March 1969): 22-38. Gojowy, Detle-f. Neue sowjetische Musik der 20er Jahre. Laabe Laaber-Verlag, 1980. Gojowy, Detlef. "Das transmentale Sprache der Neuen Musik." Musik-Konzepte 32/33. Aleksandr Skrjabin und die Skrjabin isten, edited by Heinz-Klaus Metzger and Rainer Riehn, 127 144. Munich: Edition Text + Kritik, 1983. Gojowy, Detle-f. "Hal-f Time -for Nikolai Roslavets (1881-1944): A Non-Love Story with a Post-Romantic Composer." In Russian and Soviet Musi a Essays for Boris Schwarz. Edi• ted by Malcolm Hamrick Brown, 211-220. Ann Arbor, Michi• gan: University Microfilm International Research Press, 1984. Goldstein, Michael. "Skrjabin und die Skrjabinisten. Das Schaffen Skrjabins und seiner Nach-folger — Induktion und Deduktion." Translated from Russian by P. Ruhl. In Musik Konzepte 32/33. Aleksandr Skrjabin und die Skrjabinisten, edited by Heinz-Klaus Metzger and Rainer Riehn, 178-190. Munich: Edition Text + Kritik, 1983. 184 Montagu-Nathan, Montagu. Contemporary Russian Composers. London: Cecil Palmer and Hayward, 1917; Westport, Connec• ticut: Greenwood, 1970. Perle, George. Serial Compos i t i on and Atonality. 4th rev. ed. Berkeley, Los Angeles: University of California Press, 1977. Perle, George. "Scriabin's Self-Analyses." Music Analysis. 3/2 (July 1984): 101-124. Riemann Musiklexikon: £rg'anzungsband, 1975 ed. S.v. "Rosslawets, Nikolaj Andrejewitsch." Roslavets, "Nik. A. Roslavets o sebe i svoem tvorchestve." Sovremennaia muzyka 5 (1924): 132-138. Translated in Gojowy, Neue sowjetische Musik der 20er J afire (Laaber: Laabei—Verlag, 1980), 395-400. Sabaneyeff CSabaneevJ, Leonid. Modern Russian Composers. Translated by Judah Joffe. New York: International Publishers, 1927; Da Capo, 1975. Salzman, Eric. Twentieth-Century Music: An Introduction. 2d ed. Englewood Cliffs, New Jersey: Prentice-Hall, 1974. Saminsky, Lazare. Music of Our Day: Essentials and Prophe• cies. New York: International Publishers, 1927; Da Capo, 1975. Samson, Jim. Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920. London: J. M. Dent and Son, 1977. Schibli, Sigfried. Alexander Skrjabin und seine Musik. Grenz- uberschre itungen eines prometheischen Geistes. Munich, Zurich: R. Piper and Co. Verlag, 1983. Scholes, Percy A^ ed. The Oxford Companion to Music. 9th ed. New York, Toronto: Oxford University Press, 1955. Schwarz, Boris. Music and Musical Life in Soviet Russia: Enlarged Edition 1917-1981. 2d. en 1. ed. Bloomington, Indiana: Indiana University Press, 1983. Slonimsky, Nicholas, ed. Baker's Biographical Dictionary of Musicians, 7th ed. S.v. "Roslavetz, Nicolai." Taruskin, Richard. "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'." Journal of the American Musico- logical Society 38/1 (Spring 1985): 72-142. The New Grove Dictionary of Music and Musicians, 6th ed. S.v. "Roslavets, Nikolay Andreyevich," by Detlef Gojowy. 185" APPENDIX A Chronological List o-f Works by Roslavets This chronological listing of works by Roslavets, -followed by a classification by genre, represents an amalgamation o-f the -following listings: Gojowy, Neue sowjetische Musik, 327-329; Gojowy, "Half Time," 217-219} Gojowy, "Roslavec," Die Musik- forschung, 22/1: 36-38; Grove Dictionary, 6th ed., s.v. "Roslavets" (by Gojowy); and Die Musik in Geschichte und Gegen- watrt CMGG3, s.v. "Roslawetz" (by Guido Waldmann). This present listing is the most complete of any published, to date. Dates with square brackets indicate approximate dates of composition; in some cases, only the decade has been estimated. If the date of composition is not known or cannot be approximated, the date of publication (e.g., pub. 1925) is indicated. With songs, the name of the poet is given in parentheses, and a piano accompani• ment is assumed. For most unpublished works, an indication of extant manuscripts is given, with the Soviet library in which these are located (i.e., Central State Archive for Literature and Art CCSALA3; Glinka Museum of Musical Culture CGMMC3; Moscow Conservatory Library CMCL3; Lenin Library, Moscow CLLM3). 186 1907 nenuet -for String Quartet. CSALA. Reverie -for Violin and Orchestra. Score. CSALA. 1908 Romance, Reverie, Morgenstimmung, Sonata (beginning), Gavotte, Elegie, Serenade, etc. Pieces for violin and piano. CSALA. 1909 Serenada -for Two Violins. CSALA. 1909- 3 Poemes and Romance-arabesque -for Violin and Piano. 1910 CSALA. C 1910s] 1/ chasy novoluniia CIn the Hours o-f the New Moon]. Sym• phonic poem -for large orchestra. Score with parts. CSALA. Liricheskaia poemaJPoeme lyrique -for Violin and Piano. CSALA. 1910 String Quartet. GMMC. Symphony in C Minor. Score. CSALA. 1912 Tantsy belykh dev/Danses des vierges blanches -for Violin and Piano. CSALA. Heaven and Earth. Cantata, after Byron. Unpublished, apparently lost (included in MGG and Gojowy listings). 1913 Premier Ouatuor a cordes; also Quartet/Quatuor No. 1, •first violin part, at CSALA.) Tri sochineniia CThree Compositions]. Songs: 1."Sumrak tikhii" (V. Briusov); 2."Ty ne ushla" (A. Blok); 3.-Vetere naletite" (A. Blok). Grustnye peizazhy CPaysages tristes] (Verlaine). Songs: 1. "Osenniaia pesnia" (Russian trans. N. Minskii); 2. "Zakat" (Russian trans. V. Briusov); 3."B1agos1ovennyi chas." Noktiurn/Nocturne. Harp, oboe, two violas, violon- ce1lo. 1913- Sonate pour violon et piano. 1914 Chetyre sochineniia [Four Compositions]. Songs: 1."Margaritki" (I. Severianin) 1914; 2."Vy nosite liubov" (K. Bol'shakov) 1913; 3."Volkovo kladbishche" (D. Burliuk) 1913; 4."Kuk" (V. Gnedov) 1914. 1914 Trois compositions pour piano. 187 1914 Tri Et iuda/Tro is Etudes pour piano. 1915 D\/a sochineni ia/Deux compositions pour piano. "Quasi prelude," "Quasi poeme." Prelude pour piano. Poema. Violin and piano. Pub. 1915. Pesenka Arlekina [Harlequin's Little Song] (E. Guro). Song. 1916 Quartet, second and third movements. Score; piano score. CSALA. 1917 Sonata No. 2 -for Violin and Piano. CSALA. Quartet No. 2. Incomplete score. CSALA. 1919- Five Preludes. Piano. 1922 [1920s] 7 Pieces far Violin and Piano: Etude mortelIe, Etude in Eb Major, Canon, Pugar Adagio, Pre Iiud i i a, Pomant i cheskai a poema [Romantic poema]. CSALA. [1920s Orchestral work, without title. Lento. Unfinished -1930s] score. CSALA. Orchestral work, without title. Unfinished score. CSALA. 1920 Dve Poemy/Deux Poemes. Piano. Third Quartet. Trio No. 2. CSALA. 1921 Sonata. Violoncello and piano; also, Sonata for Violoncello and Piano at GMMC. Trois Danses. Violin and piano. Paxdum'e/ Meditation. Violoncello and piano. Third Trio. Violin, violoncello, piano. Man and Sea. Symphonic poem, after Baudelaire. Unpublished, apparently lost (included in MGG listing). 1922 Symphony in four movements. Without beginning and ending. Score. CSALA. (Grove Dictionary, 6th ed., s.v. "Roslavets," indicates unpublished symphony, 1922.) 188 1922 Sonata No. 2 -for Violoncello and Piano. CSALA. World's End. Symphonic poem, after Laforgue. Unpub• lished, apparently lost (included in MGG listing). 1923 Symphony No. 2 -for Orchestra and Chorus. Unfinished score and sketches. CSALA. Sonata No. 5. Piano. 1924 Fourth Sonata. Violin and piano. (Pub. 1924.) Piano Quintet for Two Violins, Viola, Violoncello, and Piano. Score. CSALA. 1925 Violin Concerto. Arranged for violin and piano. Poslednee chudo (A. Andreev). Agit-prop, song (baritone voice). (Pub. 1925.) LLM. Contributions to agitation-propaganda song cycles (pub. 1925-26) Song cycle Pesni rex/oliutsii [Revolutionary Songs! : l."Na pervoe maia" (P. Oreshin). (Baritone voice.) (Pub. 1925); 2. "Na poliach" (P...Oresh i n) . Choir a cappella. (Pub. 1925); 3."Oktiabr'" (S. Rodov). Choir a cappella. (Composed 1924.) LLM. Song cycle Poeziia rabochikh professii [Poetry of the workers' calling]: l."Tkach" (Litkovsky). (Middle voice.) (Pub. 1925); 2."Shveia" (G. Korenev). (Pub. 1926.) LLM. 3."Tokaria" (A. Tverdyi). Choir a cappella. (Pub. 1926.) Song cycle Pesni o 1905 gode [Songs of the year 19053: 1. "Smolkli zalpy ..." (E. Tarasov). (Pub. 1925); 2. "Mat' i Syn" (G. Galinaia). (Pub. 1926.) LLM. Song cycle Dekabristy [The Decembrists]: 1."Poslanie v Sibir' dekabristam" (A. Pushkin). (Pub. 1925.) MCL; 2."Otvet' na poslanie v Sibir'" (F. Odoevskii). (High voice.) (Pub. 1925.) LLM. 1926 Chamber Symphony. Unfinished piano score with notes for orchestration. CSALA. Sonata for Viola and Piano. CSALA. 189 1926 Gimn sovetskoi raboche-krest' ianskai militsii [Hymn of the Soviet workers' and peasants' militia] (Viatich- Berezhnich). Wind band and chorus, orchestra ad. lib. 1927 Trio. Violin and viola parts. CSALA. Concerto -for Violin and Orchestra, in -four movements. Without beginning. Piano score. CSALA. 1928 Concerto No. 1 -for Violin and Orchestra. Sketches -for violin-piano score. CSALA. KomsomoI'skaia. Symphonic Poem -for Orchestra, Chorus, and Piano Solo. Sketches -for score. CSALA. Sonata No. 1 -for Viola and Piano. Incomplete. CSALA. 1929 Bab'ia dolia (P. Druzhinin). Agit-prop. song. LLM. Kon'ki 1929- Quartet. Fragments o-f score. CSALA. 1931 C 1930s! Sonata No. 2 -for Viola and Piano. CSALA. Uzbekistan. Symphonic Poem. Piano score with notes •for orchestration. CSALA. Orchestral work. Unfinished score. CSALA. Pakhta [Cotton peasant]. Ballet. (Listed in Gojowy, "Half Time," 215) . 1930 Stuchite! KOMSOMOL [Communist Youth Group] March (I. Utkin). 1932- Geroi'a [Song of the Hero]. Song arranged for 1933 orchestra. CSALA. 1934- Quartet for Four Domras, on themes of Chechen folk 1935 songs. Score. CSALA. 1935 Invention and Nocturne for Violin and Piano. CSALA. Dance for Violin and Piano. GMMC. Kolybel'naia [Lullaby] for Violin and Piano. GMMC. Scherzo for Violin and Piano. GMMC. Valse for Violin and Piano. GMMC. 190 1936 Concerto for Violin and Orchestra, in three movements. Score. CSALA. 1939 Quartet No. 4. Unfinished score. CSALA. Potpou.fr-f-Fantasie, on themes of Soviet popular songs, for Xylophone and Piano. CSALA. 1940 Legends for Violin and Piano. CSALA; also Legenda for Violin and Piano in D minor, n.d., at GMMC. 1941 Quartet No. 5 in Eb Major. GMMC. 1941- 24 Preludes for Violin and Piano. GMMC. 1942 \ 1942 Tabachok (A. Prishelets). Agit-prop song. LLM. n.d. Rondo and Polonaise for Violin and Piano. GMMC. 191 Listing o-f Works by Genre A.Orchestral Works Reverie -for Violin and Orchestra. 1907. Symphony in C Minor. 1910. 1/ c/tasy novoLun i ia. Symphonic poem -for large orchestra, t1910s.3 nan and Sea. Symphonic poem, after Baudelaire. 1921. Unpublished, apparently lost. Symphony in -four movements. 1922. Without beginning, ending. World's End. Symphonic poem, after Jules Laforgue. 1922. Unpublished, apparently lost. Symphony No. 2 for Orchestra and Chorus. 1923. Unfinished. Violin Concerto. Arranged for violin and piano. 192S. Chamber Symphony. 1926. Unfinished. Concerto for Violin and Orchestra, in four movements. 1927. Without beginning. Concerto No. 1 for Violin and Orchestra. 1928. Sketches for violin-piano score. KomsomoI'skaia. Symphonic Poem for Orchestra, Chorus, and Piano Solo. 1928. Sketches for the score. Orchestral work, without title. Lento. C1920s-1930s.3 Unfinished. Orchestral work, without title. C1920s-1930s.3 Unfinished. Pakhta. Ballet. C1930s.3 Uzbekistan. Symphonic Poem. C1930s.3 Orchestral work. C1930s.3 Unfinished. Geroia. Arranged for orchestra. 1932-33. Concerto for Violin and Orchestra, in three movements. 1936. 192 B.Solo and Chamber Works 1.Works -for Solo Piano. Trots Compositions pour piano. 1914. Tri Etiuda/Trois Etudes pour piano. 1914. Dva sochineniia IDeux Compositions pour piano. 1915. Prelude pour piano. 1915. Five Preludes. 1919-1922. fli/e Poemy/Deux Poemes. 1920. Sonata No. 5. 1923. (No indications o-f other piano sonatas.) 2.Sonatas for Violin and Piano. (Grove Dictionary, 6th ed., s.v. "Roslavets," indicates that -five violin sonatas were written.) Sonate pour violon et piano. c. 1913-1914. Sonata No. 2 -for Violin and Piano. 1917. Fourth Sonata. Pub. 1924. 3.Other Works -for Violin and Piano. Pomancet Reverter Morgenstimmungf Sonata (beginning), Gavotte, E leg ie, Serenade, etc. Pieces -for violin and piano. 1908. 3 Poemes and Romance-arabesque for Violin and Piano. 19O9-1910. Liricheskaia poema/Poeme lyrique for Violin and Piano. C1910s.3 Tantsy belykh dev/Danses des vierges blanches for Violin and Piano. 1912. Poema. Pub. 1915. 7 Pieces -for Violin and Piano: Etude mortelle, Etude in Eb Major, Canon, Fugat Adagio, Pre Iiudiia, Romanticheskaia poema. C1920s.3 193 7rot's Dansss. 1921. Invention and Nocturne for Violin and Piano. 1935. Dance -for Violin and Piano. 1935. Ko lyt>e I'nsi's -for Violin and Piano. 1935. Scherzo -for Violin and Piano. 1935. i/alse -for Violin and Piano. 1935. Legends -for Violin and Piano. 1940. (Also Legends for Violin and Piano in D minor. n.d.; likely the same work) 24 Preludes for Violin and Piano. 1941-42. Rondo and Polonsise for Violin and Piano. n.d. 4.Sonatas for Viola and Piano. Sonata for Viola and Piano. 1926. Sonata No. 1 for Viola and Piano. 1928. Incomplete. Sonata No. 2 for Viola and Piano. C1930s.3 5.Sonatas and Other Works for Violoncello and Piano. Sonata. 1921. Sonata for Violoncello and Piano. 1921. Pszdum'et Ned i tst i on. 1921. Sonata No. 2 for Violoncello and Piano. 1922. 6.Piano trios. Trio No. 2. 1920. Third Trio. For violin, violoncello, and piano. 1921. Trio. Violin and viola parts. 1927. 194 7.String Quartets. Nenuet for String Quartet. 1907. String Quartet. 1910. Quartet/Quatuor No. 1. First violin part. 1913. Premier Quatuor a cordes. 1913. Quartet, second and third movements. 1916. Quartet No. 2. 1919. Incomplete. Third Quartet. 1920. Quartet. 1929-1931. Fragments of score. Quartet No. 4. 1939. Unfinished. Quartet No. 5 in Eb Major. 1941. 8.Other Miscellaneous Chamber Works Serenada for Two Violins. 1909. NoktiurnJNocturne. Harp, oboe, two violas, violoncello. 1913. Piano Quintet for Two Violins, Viola, Violoncello, and Piano. 1924. Quartet for Four Domras, on themes of Chechen folk songs. 1934-1935. Potpourri-fantasi'e, on themes of Soviet popular songs, for Xylophone and Piano. 1939. C.Vocal Works 1.Choral Works. Heaven and Earth. Cantata, after Byron. 1912. Unpublished, apparently lost. From song cycle Pesni Revo I iutsi i'. "Na poliakh" (P. Oreshin). Choir a cappella. (Pub. 1925)5 "Oktiabr*" (S. Rodov). Choir a cappella. 1924. 195 From song cycle Poeziia rabochikh professii'. "Tokaria" (A. Tverdyi). Choir a cappella. 1926. Simn sox/etskoi raboche-krest' ianskoi militsii (Viatich- Berezhnich). Wind band and chorus, opt. orchestra parts. 1926. 2.Songs for Voice and Piano. Tri sochineniia. 1913. l."Sumrak tikhii" (V. Briusov); 2. ne ushla" (A. Blok); 3."Vetere naletite" (A. Blok). Srustnye peizhazy (Verlaine). 1913. l."Osenniaia pesnia"; 2."Zakat". 3."B1agos1ovennyi chas." Chetyre soch inert iia. 1913-1914. 1. "Margar i tk i " (I. Severianin). 1914J 2."Vy nosite liubov" (K. Bol'shakov). 19135 3."Volkovo kladbishche" (0. Burliuk). 1913; 4."Kuk" (V. Gnedov). 1914. Pesenka ArZekina (E. Guro). 1915. 3.Agitation-propaganda songs. Poslednee chudo (A. Andreev). Baritone voice. (Pub. 1925. From song cycle Pesni Pewo I i utsi i'. "Na pervoe maia" (P. Oreshin). Baritone voice. (Pub. 1925.) From song cycle Poeziia rabochikh professii'. "Tkach" (Litkovsky). Middle voice. (Pub. 1925); "Shveya" (G. Korenev). (Pub. 1926.) From song cycle Pesni o 1905 gode: "Smolkli zalpy. . ." From song cycle Dekabristy. "Poslanie v Sibir' dekabristam" (A. Pushkin). (Pub. 1925); "Otvef na poslanie v Sibir'" Odoevskii). High voice. (Pub. 1925.) Bab' ia dolia (P. Druzhinin). 1929. Kon'ki (A. Shiriaevets). 1929. Stuchite.' (KOMSOMOL-March) (I. Utkin). 1930. Tabachok (A. Prishelets). 1942. i ^t. APPENDIX B This appendix provides a brief examination o-f issues of PC content tangential to the discussions in Chapter Two. T-level Identities o-f Individual Harmonies in "I", Measures 6-8 \ . • A further, conceivable explanation of T-level identity in mm. 6-8 of "I" involves designating each harmony with a T-level of most similar PC content, with individual harmonies conforming to the T-O,T-2,T-7 transpositional relationship assumed for mm. 6, 7, and 8, respectively (Ex. 6-1). Example 6-1. Collections in mm. 6-8 and the most similar T- 1 eveIs. (6) 4TH J'-TIHE-SPAHJ 5TH .P-TIHE-SPAHi 6TH J'-TINE-SPAN T-O 15) T-l (5) T-O (5) T-9 (5) T-4 (5) T-7 (6) 197 Example 6-1 continued. 171 4TH 7-TIHF.-SPMII 5TH J'-TIflE-SPAHl 6TH /-TIME-SPAR is ZLT. f T-2 1S1 T-3 (31 / T-ll 131 T-2 (3) / T-6 (3) 7 T-9 (61 (81 1ST j'-TINE-SPAR| 210 J'-TIK-SPAMJ 3RD ^-TIRE-SPAN ) 1 J - L o rz—i bo a ° °\ T-7 (3) T-8 (5) T-7 (51 tt»** T-4 (31 T-ll (31 T-2 (61 Note:. PCs in T-levels that match the collection's PCs are lis• ted as whole notes, with the number o-f common PCs being given i brackets. Moreover, the -first and third collections of m. 6, second half (and likewise of m. 7, second half, and of m. 8) have four PCs out of six in common, as do the second and third. Because of these common PCs and because the middle collection of each group of three tends to function as an auxiliary, decorative collection (a function that is easily perceived since many PCs of these middle collections are approached and/or left by step) 198 the outer collections o-f each group o-f three are designated as the same T-level. The T-level succession thus adduced -for mm. 6-8 is: T-ll,T-0,T-l/T-9,T-0 (m. 6), T-11,T-2,T-3/T-11,T-2 (m. 7), T-7, T-8/T-4, T-7 (m. 8). Such a succession o-f T-levels reflects! the application o-f individual collections rather than subsets o-f an enlarged ICC; the T-0,T-2,T-7 transpositional relationship o-f mm. 6, 7, and 8; a consistency o-f T-level sequence in the three measures; and the similarity o-f the -first and third collections o-f each time-span, as noted above. Gojowy's Analysis o-f T-Levels in "III" Gojowy's -four ICCs o-f "III" include the -four most -frequent• ly occurring PC collections or transpositions thereof. His sequence of ICCs and their T-levels is illustrated in Fig. 6-1. 199 Figure 6-1. T-level successions in "III", as given in Gojowy'5 analysis. (a)ICCs of "III": 7 •b- (b)T-level successions in "III": MEASURE 111 [21 13) ICC, T-LEVEL i,0—a,3 c,0—c,7—c,ll—e,2 IRRE6ULAR—b, 1—b,4 (a,l/b,l) H. (41 15-61 171 181 (91 (10-111 ICC, T- b,7—b,0™b,3 4,0-—c,3-—c,6—*,( )—4,1 c,6 (a,5) N. (121 113) (14-131 ICC, T- a,3—IRRE6ULAR—-c,9—c,4—c,8—c,ll c,4 (•,0 TIMERS'*) There is, however, a compromise of Goj owy's system of four ICCs that is more practical. The similarities between ICCs "a" and "b", and between ICCs "c" and "d" (in either case with only one PC that differs), are such that two of the ICCs could be cited instead of four; "a" and "d" are more inclusive. Figure 6-2a presents the two ICCs; the altered sequence of T-levels is given in Fig. 6-2b. 200 Figure 6-2. ICCs "a" and "d" in "III". (a)Modi-fied ICCs: "aO" : Db-D*t-E-F-G-Gtt— Bb — B "cO": Eb-E-Gb-G-Bbb-B "bO" : Db-Dtt-E-F-G-Gtt B "dO": Eb-E-Gb-G-Bbb-B — Db "new "new aO": Db-Dtt-E-F-G-G**- (Bb) -B dO": Eb-E-Gb-G-Bbb-B-(Db) ICAs: 2—1-1-2-1 3 2 1-2—1-2 2 4 (2 +1) (2 + 2) (b)T-levels o-f ICCs "a" and "d": n. [1] (21 (31 (41 (5,6] ICC, T- a,0 a,5 d,0 4,7 df11 4,2 a,l a,l a,4 a,7 a,0 a,5 4,0 M. (71 (81 [9] [10,111 (121 [131 (14,13] ICC, T- 4,3 4,6 4,10 4,1 4,6 a,5 4,0 4,9 4,4 4,8 4,11 4,4 (c)T-level occurrences and total time-spans: ICC, T- aO al a4 a5 a7 a( I OCCURRENCES 2 2 1 3 1 9 TOTAL TINE-SPAN (8TH VALUES): 4 5 1 8 2 20 ICC, T- 40 41 42 43 d4 46 47 48 49 410 dll d( I OCCURRENCES 3 1112 2 1111 2 16 TOTAL TINE-SPAN 14 6 1 9 9 10 1 2 2 3 3 60 This system o-f two ICCs represents a compromise between Gojowy's -four (i.e., the most -frequently occurring PC collec• tions and transpositions thereof, with no variant elements), and Perle's use o-f a single ICC with three variant elements not occurring with every collection. An examination o-f locations and -functions o-f variant ele• ments (i.e., represented by the bracketed PCs in ICCs "a" and "d", Fig. 6-2a) establishes no consistent relationship between 201 these elements and their location and function in the music. Figure 6-2c shows the occurrences and total time-spans of ICC T-levels in order to establish which of the collections can be considered more significant. In this light, T-levels "dO" and "d6" (and to a lesser extent "d3" and "d4") can be identified as of greater significance. An Analytical Alternative: A Single ICC for "I", "II", and "III" Similarity of content makes it possible to analyze the har• monic successions of the three pieces in terms of a single ICC including elements "0", "3", "4", "6", and "8". If the initial T-level of this common ICC, occurring as the first harmony of "I", were to be designated as T-O, then the first T-level of "II" would be T-ll, and the first T-level of "III" would be T-5. There are obvious analytical advantages in using a single common ICC; however, there are some problems with this method. The use of a single common ICC implies that initiating harmonies in two of the three pieces are somehow subordinate to that of the piece whose initial T-level is designated as T-O. And since there are differences in variant elements associated with each piece (e.g., element "IO" in "I", "1" in "II", and "9", "IO", and "11" in "III"), and in the extent of their use, and also differences in the notational orthography of ICC T-levels in the music, par• ticularly that of "III", three individual ICCs are taken as a basis for analyses in this thesis. 202 Prolongation o-f T-Levels Reiterated T-levels, with only a -few harmonies separating occurrences, imply a prolongation of the T-levels and their con• sequent, special significance. PC invariance and pitch-class continuity can play a role in the perception o-f prolongation, this perception being facilitated when: there are no more than three or four interpolating T-levels; the vertical position or register of reiterated pitches remains the same in both appear• ances of the T-level; pitches in the recurring T-level appear also in the interpolated T-levels, preferably in the same regi• ster; the reiterated T-levels appear on stranger metric time- points, and/or have similar rhythmic patterns; and both appear• ances of the reiterated T-level are given similar forms of emphasis, exposure, accentuation, or articulation. Example 6-2 presents prolonged T-levels, with the musical notation of these illustrating invariant PCs and pitch continuity. 203 Example 6-2. Prolonged T-levels in Trois Compositions. 204 Example 6-2 continued. (101 (ill [121 T-3 T-6 T-3 T-9 T-4 T-9 5(2) 5(2) 4(2) 412) —en— r-jr-e- 1 1_ 0—\ 1 1 0—| 1 i ! 11 »>• 1 "IVll OS*? 1 n 1 ——i - • . I 1 MEASURE 3 4 7 1 10 11 12 13 T-LEVELS 10-3 10-3.... 10-3 0-5....0-5 0-3 0 0 PROLONGED [10 10 101 10 0 0 0—0J LEVELS: [3- 3 31 (5...... 5 31 20S Example 6-2 continued. •Ill* MEASURE 2 3 4 8 9 10 12 13 14-15 T-LEVELS 8—3—7—10 1-4 7-0-3 2-6 9 2 5-0 5-0-4-7 0 PROLONGED [7 71 12——21 (0 0 01 LEVELS 15.... 5 51 206 Nate: Lines in the -first a-f two staves with each example o-f prolongation connect invariant PCs in adjacent harmonies. The unbracketed and bracketed numbers above each harmonic succession indicate the number o-f invariant PCs and the number o-f pitch continuities, respectively. On the second o-f two staves, horizontal lines illustrate invariance o-f PCs o-f the prolonged T-levels through interpolated T-levels. Given the above-stated conditions, T-levels T-ll (mm. 6-7), T-3 and T-6 (mm. 10-11), and T-9 (m. 12) in "I", T-10 and T-3 (mm. 3-4), and T-0 and T-5 (mm. 10-11), and T-2 (mm. 8-11) in "III" are particularly convincing, while other reiterated T- levels less easily interrelated as prolongations.